Geometric Behavior Research Articles

Anisotropic charged compact stellar configurations in the perspective of gravitational decoupling approach

We construct the physically admissible charged compact star models threaded with anisotropic matter contents via gravitational decoupling approach. Durgapal IV solution containing charge is considered as seed solution for applying minimal geometric deformation approach. We extend the isotropic seed solution into anisotropic domain by imposing suitable mimic constraints on the physical variables i.e. pressure and density. The extended solution is employed to frame the models of dense relativistic structures. We study the geometrical and thermodynamic behavior of the models and examine the physically admissible attributes of the models via graphical patterns. The stability status of the compact entities is examined through different stability criteria. The essential energy bounds are found to be satisfied within the compact star models. We performed the extensive analysis of the model for the star RXJ 1856-37 having mass 0.9 M Θ and radius 6 km. The extended anisotropic solution is also compatible with observed masses as well as radii of some compact stars EXO 1785-248 and PSR J1614-2230.

Analytical estimation of the key performance points of the tensile force-displacement response of Crescent Shaped Braces

The technical note investigates the tensile force-displacement response of the hysteretic steel yielding brace known as Crescent Shaped Brace and characterized by a boomerang-like geometrical shape. The force-displacement curve is governed by three key performance points which correspond to the transition points separating the initial elastic behaviour, the flexural plastic behaviour, the geometrical hardening behaviour and the final axial plastic behaviour.In particular, the influence of the main geometrical parameter of the device, the so-called “lever arm”, on the strongly non-linear force-displacement behavior is analyzed by means of a simplified kinematic model. Based on this, analytical estimations of the key performance points are derived and compared with numerically simulated force-displacement curves.

A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space

Suppose p n be sequence of positive reals. By H w p n , we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞ , for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in H w p n .

Geometric magnonics with chiral magnetic domain walls

Spin wave, the collective excitation of magnetic order, is one of the fundamental angular momentum carriers in magnetic systems. Understanding the spin wave propagation in magnetic textures lies in the heart of developing pure magnetic information processing schemes. Here we show that the spin wave propagation across a chiral domain wall follows simple geometric trajectories, similar to the geometric optics. And the geometric behaviors are qualitatively different in normally magnetized film and tangentially magnetized film. We identify the lateral shift, refraction, and total reflection of spin wave across a ferromagnetic domain wall. Moreover, these geometric scattering phenomena become polarization-dependent in antiferromagnets, indicating the emergence of spin wave birefringence inside antiferromagnetic domain wall.

Adaptation of the Newton-Raphson and Potra-Pták methods for the solution of nonlinear systems

In this paper we adapt the Newton-Raphson and Potra-Pták algorithms by combining them with the modified Newton-Raphson method by inserting a condition. Problems of systems of sparse nonlinear equations are solved the algorithms implemented in Matlab® environment. In addition, the methods are adapted and applied to space trusses problems with geometric nonlinear behavior. Structures are discretized by the Finite Element Positional Method, and nonlinear responses are obtained in an incremental and iterative process using the Linear Arc-Length path-following technique. For the studied problems, the proposed algorithms had good computational performance reaching the solution with shorter processing time and fewer iterations until convergence to a given tolerance, when compared to the standard algorithms of the Newton-Raphson and Potra-Pták methods.

Quasi-static numerical simulation of the dynamic launching process for high-altitude balloon

In this paper, by establishing a set of mathematical models and computing methods, the numerical simulation of the ground dynamic launching process under the quasi-static assumption for a high-altitude balloon system is conducted to reveal the rich mechanical and geometric behaviors involved in it. The mathematical model includes the solution of the bubble shapes and the kinematic analysis, as well as the static model of the “membrane bundle system”. Considering the middle and lower region of the bubble still meet the zero circumferential stress condition under the hydrostatic pressure gradient, the upper fully expanded shape generatrix is the same as the balloon generatrix of the ceiling height. The multiple shooting method combined with Sequential Quadratic Programming (SQP) is used to solve the lower partially expanded bubble generatrix. Based on the force balance equations of the microelement in “membrane bundle system”, and considering the friction force in contact with the horizontal ground and the characteristics that the membrane bundle is a variable mass system along the arc length direction, the “multiple shooting method + SQP” method is still used to solve the shape and internal force of the “membrane bundle system” under two end geometric boundary conditions. In co-simulation, taking the dynamic launching process of the zero-pressure balloon system with the ceiling flight height of 30 km and hanging a load of 300 kg as the object, under the conditions of 1.5 m/s and 4.5 m/s wind speeds, the initial layout and the rising process of dynamic launching is calculated. Through the analyses of the simulation results, four stages of the rising process are concluded, namely, the stage of the “membrane bundle system” relaxation and falling to the ground, the longitudinal rising stage, the main rising stage, and the straightening stage. The geometry and force characteristics of the bubble and the “membrane bundle system” are discussed to provide a reference for the simulation of the actual high-altitude balloon ground dynamic launching testing.

A first-principles study of Ag clusters adsorption on porphyrin-like N4[sbnd]CNT: Geometric and electronic properties

Using first-principles theory, this paper investigates the Agn-clustering (n = 1~4) effect on the geometric and electronic behaviors of N4CNT. The band structure, density of state, total charge density, charge density difference and frontier molecular orbital theory are used to comprehensively understand the physicochemical properties of AgnN4CNT. Our results indicate that the binding force of Agn clusters become stronger after their adsorption, which behaves as electron donators redistribute the electron density of the whole systems largely, deforming the electronic behavior of N4CNT and enhancing the electrical conductivity of the whole systems. Besides, Ag3N4CNT is the most stable and the easiest to be generated among AgnN4CNT systems, which can be grown from Ag2N4CNT attaching another single Ag atom or the detachment of Ag4N4CNT releasing an Ag atom, as further supported by the FMO analysis. The magnetic property of Ag1 and Ag3 clusters after adsorption are weakened while Ag2 and Ag4 clusters remain nonmagnetic behavior. Our work means to shed light on the physicochemical properties of AgnN4CNT to help explore its potential application in the future.

Spatial analysis of harsh driving behavior events in urban networks using high-resolution smartphone and geometric data

The aim of the present study is to conduct spatial analysis of harsh events of driving behavior across road segments of an urban road network. The adopted approach involved automating the segment characteristic extraction process for the urban network study area. Subsequently, naturalistic driving big data from an innovative smartphone application were map-matched to the segments that each driver traversed, and thus geometrical, road network and driver behavior spatial data frames were obtained per road segment. Global and local Moran's I coefficients were calculated based on a nearest-neighbour scheme, and indicated the presence of a certain degree of positive spatial autocorrelation both for harsh brakings (HBs) and for harsh accelerations (HAs). Furthermore, the creation of empirical and theoretical spherical variograms indicated that on average, about 190 m from each road segment centroid there is no observable spatial autocorrelation for HBs; the respective distance is 200 m for HAs. Geographically Weighted Poisson Regression (GWPR) models were used to model harsh event frequencies. Segment length and pass count are positively correlated with HB frequencies, while gradient and neighbourhood complexity are negatively correlated with HB frequencies. Curvature, segment length, pass count and the presence of traffic lights are positively correlated with HA frequencies. Road type and lane number were found to have a more circumstantial effect overall.

BULK VISCOUS BIANCHI TYPE I BAROTROPIC FLUID COSMOLOGICAL MODEL WITH VARYING Λ AND FUNCTIONAL RELATION ON HUBBLE PARAMETER IN ROSEN’S BIMETRIC GRAVITY

We have deduced that bulk viscous Bianchi type I barotropic fluid cosmological model with varying $\Lambda$ and functional relation on hubble parameter by solving the field equations bimetric theory of gravitation. It is observed that our model has exponentially accelerating expansion at late time starting with decelerating expansion which agreed the observation of Perlmutter (1998), Knop (2003), Tegmark (2004) and Spergel (2006). In the beginning, our model has more than three spatial-dimensions then it switched over to three-dimensional spatial geometry at late epoch of time and it is agreed with Borkar et al. (2013). Other geometrical and physical behavior of the model have been studied.

The influence of river point bars on flood hydraulic using geometric model

Points bar formation has an important role to changing the hydraulic behavior during floods. In this study, topographic maps at 1:1000 scale for 40 km. given reach of river channel were used in HEC-GeoRAS and HEC-RAS softwares to simulate the geometric features and hydraulic behavior. The hydraulic behavior of Haraz river located in northern Iran, with 25 years of flood data was simulated in two scenarios of present channel conditions and without any point bar. Therefore, the effects of point bars were assessed on flood flow depth and zone, flow velocity and also water shear stress. The results indicated that the formation of point bars causes the flow resistance, its direction to the banks, accelerates erosion and increases the depth of flood. Also, point bars have increased the flood zone by reducing the flow capacity in a cross section of the river channel. Additionally, the increase in flow depth, flood zone, and water shear stress on the channel buffers were estimated 33.33, 95.57, and 66.67%, respectively. These changes are depending on the dimensions of point bars and the rate of flow reduction in a cross section of the channel given reach.

Dark energy nature of viscus universe in f(Q)-gravity with observational constraints

In this study, we have investigated the dark energy behavior of the viscus-fluid in [Formula: see text]-gravity in a flat, isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker (FLRW) space-time metric. We have considered the linear form of [Formula: see text] function as [Formula: see text] with [Formula: see text] and [Formula: see text] as model parameters. We have solved the field equations for the scale factor [Formula: see text] and found [Formula: see text], where [Formula: see text] and [Formula: see text] and [Formula: see text] is an integrating constant, [Formula: see text] is the EoS for normal matter and [Formula: see text] is generated from bulk-viscus fluid. We have calculated the several cosmological parameters for this scale factor and studied their physical and geometrical behavior along the observational data sets [Formula: see text] and Union [Formula: see text] compilation of SNe Ia data sets. We have observed that the [Formula: see text] factor reveals the presence of cosmological constant and for [Formula: see text], the acceleration drives by the bulk-viscosity of the fluid and it behaves just like dark energy model without cosmological constant. We have studied the effective EoS [Formula: see text] and found [Formula: see text]. We have evaluated the age of the present universe as [Formula: see text] Gyrs. and also, we have studied the nature of deceleration parameter with the signature-flipping point at [Formula: see text] and the present value of deceleration parameter [Formula: see text] is obtained as [Formula: see text].

Design, metallurgical features, mechanical performance and canal preparation of six reciprocating instruments.

To compare six reciprocating instruments regarding their geometric design, metallurgical characteristics, mechanical behaviour and ability to prepare root canals. A total of 246 new 25-mm NiTi instruments (41 per group) from six reciprocating systems (Reciproc, Reciproc Blue, One Files, One Files Blue, Reverso Silver, and WaveOne Gold) were evaluated throughout a multimethod approach regarding their design using stereomicroscopy (number of blades and helix angle) and scanning electron microscopy (blades symmetry, cross section and surface finishing), nickel-titanium composition, phase transformation temperatures, mechanical performance (cyclic fatigue, torsional and bending resistance) and unprepared canal surface area on anatomically matched mandibular molars assessed by micro-CT. One-way ANOVA and post hoc Tukey's or Mood's median tests were selected depending on sample distribution with significance level set at 5%. The instruments had similarities regarding their metal composition and unprepared canal area, whilst differences in phase transformation temperatures and geometric design (number of blades, surface finishing and tip geometry) were observed. Overall, no difference was observed regarding the maximum torque values (P>0.05), whilst One Files (72s) and One Files Blue (414s) had the shortest and longest times to fracture, respectively (P<0.05). Similar angles of rotation were observed in Reciproc (310°), One Files (285°) and Reverso Silver (318°) instruments (P>0.05), which were significantly lower than Reciproc Blue (492°), One Files Blue (456°) and WaveOne Gold (492°; P<0.05). Maximum bending load demonstrated that Reciproc Blue (201.3 gf) was significantly more flexible that the other instruments (P<0.05). Although there were similarities in metal composition and percentage of unprepared canal surface, the instruments had differences in the overall geometric design, phase transformation temperatures and in the four mechanical resistance parameters (time to fracture, maximum torque, angle of rotation and maximum bending load).

Kannan Contraction Operator on the Domain of r . -Cesàro Matrix in ℓ t . and Related Prequasi Ideal with an Application of Nonlinear Difference Equations

In this article, the sequence space Ξ r , t υ has been built by the domain of r l -Cesàro matrix in Nakano sequence space ℓ t l , where t = t l and r = r l are sequences of positive reals with 1 ≤ t l &lt; ∞ , and υ f = ∑ l = 0 ∞ ∑ z = 0 l r z f z / ∑ z = 0 l r z t l , with f = f z ∈ Ξ r , t . Some topological and geometric behavior of Ξ r , t υ , the multiplication maps acting on Ξ r , t υ , and the eigenvalues distribution of operator ideal constructed by Ξ r , t υ and s -numbers have been examined. The existence of a fixed point of Kannan prequasi norm contraction mapping on this sequence space and on its prequasi operator ideal are investigated. Moreover, we indicate our results by some explanative examples and actions to the existence of solutions of nonlinear difference equations.

Higher Dimensional LRS Bianchi Type-I String Cosmological Model with Bulk Viscosity in General Relativity

Objective: To present a new solution to the field equations obtained for higher dimensional LRS Bianchi type-I universe generated by means of a cloud of strings with particles connected to them with bulk viscosity in general relativity. Methods: To obtain the solutions of field equations of higher dimensional LRS Bianchi type-I universe we consider that the shear scalar of the model is proportional to the scalar expansion of the model (saq ), which leads to, c=b^n. The physical and geometrical behaviors of the model universe are studied by comparing with the present cosmological scenario and observations. Findings: It is observed that our model is anisotropic, expanding and decelerates at early stage and then accelerates in late universe giving the inflation model universe. Novelty: We obtained new solution to the field equations for higher dimensional LRS Bianchi type-I generated by means of a cloud of strings with bulk viscous fluid in general relativity. Keywords: LRS Bianchi TypeI Metric; Bulk Viscous Fluid; Strings

Precision Assembly Simulation of Skin Model Shapes Accounting for Contact Deformation and Geometric Deviations for Statistical Tolerance Analysis Method

Tolerance analysis methods, which are important to achieve a balance between manufacturing costs and functional requirements, have been studied and improved over the last 30 years. This paper proposes a new method to improve the precision of assembly simulation for statistical assembly simulation; by investigating the effect of the geometric deviations and mechanical behaviors of assembly contact on the stack-up assembly deviation by combining the recent theories on the tolerance analysis of rigid bodies and local contact deformation. To improve the precision of the tolerance analysis, real parts with form defects were simulated with the help of non-nominal skin model shapes. The SMSs were first considered to be rigid, and a quadratic optimization-based method for the rigid body displacement was used to calculate the initial contact points of all the SMSs. Next, contact deformation, following Hertzian contact theory, occurred at the initial contact points, which changed the relative positions of the SMSs in the subsequent interactions. The iteration process was convergent, and the final simulation for tolerance analysis could be generated after several iterations. Case studies demonstrated the practicality of the proposed method. Their actual assembly deviations were simulated by combining the effects of geometric deviations and local surface deformations. Since the proposed tolerance analysis framework based on statistical assembly simulation, it is expected to control the functional requirements of mechanical assemblies with much rough tolerance design and help optimize the tolerance in the future.

Numerical Validation of the Two-Way Fluid-Structure Interaction Method for Non-Linear Structural Analysis under Fire Conditions

Fire accidents on ships and offshore structures lead to complex non-linear material and geometric behavior, which can cause structural collapse. This not only results in significant casualties, but also environmental catastrophes such as oil spills. Thus, for the fire safety design of structures, precise prediction of the structural response to fire using numerical and/or experimental methods is essential. This study aimed to validate the two-way fluid-structure interaction (FSI) method for predicting the non-linear structural response of H-beams to a propane burner fire by comparison with experimental results. To determine the interaction between a fire simulation and structural analysis, the Fire-Thermomechanical Interface model was introduced. The Fire Dynamics Simulator and ANSYS Parametric Design Language were used for computational fluid dynamics and the finite element method, respectively. This study validated the two-way FSI method for precisely predicting the non-linear structural response of H-beams to a propane burner fire and proposed the proper time increment for two-way FSI analysis.

Dynamic interfacial crack propagation and kinking in sandwich panels

The dynamic interfacial crack propagation and crack kinking phenomena in sandwich panels are studied. The paper derives an analytical approach based on the Extended High-Order Sandwich Panel Theory (EHSAPT) and a cohesive interface modeling. The mathematical modeling of the panel makes a distinction between the face sheets and the core. The core is further divided into two bodies aiming to allow the nucleation of a shear crack in the core or the kinking of a core-face sheet crack into the core. The panel therefore includes four layers that are interconnected through three interfaces. The First-Order Shear Deformation Theory (FSDT) is adopted for the two face sheets and the EHSAPT is applied to the two core layers. Translational, rotational, and high order inertial effects are considered in all components. A geometrical nonlinear behavior with linear elastic laws is adopted for the face sheets while the core layers use linear kinematic relations and linear constitutive laws. The interfaces use nonlinear cohesive laws to model the dynamic nucleation, propagation, and kinking of cracks. The dynamic model is used for a numerical study of sandwich panels subjected to three point bending and end shortening loading conditions. The study explores the coupling of the crack propagation with the dynamic response. A comparison of the dynamic results with their static counterparts further explains the physical response of the sandwich panel and the dynamic characteristics of its failure mechanism.

A nonlinear geometric model for pre-stressed steel–concrete composite beams

Steel–concrete composite beams are commonly employed in civil constructions such as multi-storey building floors and long-span bridges. In case of significant span to depth ratios, excessive deflections and noticeable crack widths at the concrete slab may occur at the serviceability stage. In this context, internal or external pre-stressed tendons can be used as a remediation. In the latter case, significant effects of geometric non-linearity may arise due to the strain incompatibility between the external tendon and the composite member, resulting in a variable tendon eccentricity during deformation. In this paper, second-order effects are evaluated in eight pre-stressed steel–concrete composite beams for which experimental results are available. Hence, a three-dimensional finite element model using a Lagrangian description is proposed. The external tendons are represented by one-dimensional catenary elements, whereas the reinforced concrete slab and steel profile are modeled by shells finite elements. Slipping at the slab-beam interface and tendon-deviator locations are also included in the analysis. For the studied externally pre-stressed beams, the introduction of nonlinear geometric behavior yields lower collapses loads in relation to its linear counterpart, varying this difference between 6.4 and 9.1%.

LRS Bianchi I Model with Bulk Viscosity in $$\boldsymbol{f(R,T)}$$ Gravity

Locally-rotationally-symmetric Bianchi type-I viscous and non -viscous cosmological models are explored in general relativity (GR) and in f(R,T) gravity. Solutions are obtained by assuming that the expansion scalar is proportional to the shear scalar which yields a constant value for the deceleration parameter (q=2). Constraints are obtained by requiring the physical viability of the solutions. A comparison is made between the viscous and non-viscous models, and between the models in GR and in f(R,T) gravity. The metric potentials remain the same in GR and in f(R,T) gravity. Consequently, the geometrical behavior of the $f(R,T)$ gravity models remains the same as the models in GR. It is found that f(R,T) gravity or bulk viscosity does not affect the behavior of effective matter which acts as a stiff fluid in all models. The individual fluids have very rich behavior. In one of the viscous models, the matter either follows a semi-realistic EoS or exhibits a transition from stiff matter to phantom, depending on the values of the parameter. In another model, the matter describes radiation, dust, quintessence, phantom, and the cosmological constant for different values of the parameter. In general, f(R,T) gravity diminishes the effect of bulk viscosity.

Fabrication of customized Ti6AI4V heterogeneous scaffolds with selective laser melting: Optimization of the architecture for orthopedic implant applications

Orthopedic implants with heterogeneous porous structures were known as ideal bone osteointegration. This research introduced the selective laser melting (SLM), finite element analysis (FEA), and a hydrothermal process (HT) for manufacturing a three-level heterogeneous porous structure. The macroporous structure was designed via CAD and micropores were tuned via laser power regulation. A nano-size layer of hydroxyapatite crystals was coated by an HT process. The mechanical properties were reinforced via a core-shell structure with core reinforcement. The existence of micropores and nano-hydroxyapatite coating enhanced the in vitro proliferation of preosteoblasts and osteogenic cellular behaviors of rBMSCs. Thus, the three-level heterogeneous porous titanium implants could inspire researchers with potential clue of cyto-implant interaction mechanism, therefore building ideal orthopedic implants with accelerated osteointegration. Statement of significancePorous structures of titanium implants play an important role in bone tissue regeneration; The geometrical environment influence cell behaviour and bone tissue ingrowth in all macro-/micro-/nanoscale. In this study, a novel method to fabricate heterogeneous scaffolds and its macro-/micro-/nanoscopic structures were studied. A CAD model was used to obtain the macroscopic structure and the insufficient laser power was introduced for porous microstructure. Therefore, a layer of nano hydroxyapatite was coated via hydrothermal process. Cytoproliferation and cytodifferentiation results indicated that a integrity of regular/irregular, macro-/micro-/nanoscale porous structure had advance in recruiting stem cells and promoting differentiation. This research is beneficial to the development of bone implants with better bone regeneration ability.