Conical System Research Articles

Advanced golden jackal optimization-based fractional-order integral terminal sliding-mode (FO-ITSM) controller for level control of the conical tank system

This article examines a conical tank nonlinear system's level control. A crucial component of facilities like milk processing plants and sugarcane mills is the conical tank. The fluid drains entirely due to the conical shape of the tank. The conical form of the system causes nonlinear dynamics. The conical tank nonlinear system transfer mechanism is not easily accessible, and different operating heights require different transfer mechanisms, making controller design difficult. Developing the Fractional-Order Integral Terminal Sliding-Mode (FO-ITSM) Controller system for Advanced Golden Jackal Optimisation (GJO) based conical tank systems is the main objective of this paper. This is utilised to deliver real-time liquid level management in non-linear conical systems. The dynamics of these models make it possible to identify the conical tank system that produces control signals from liquid samples taken at reference levels with greater accuracy. This system, which is employed on multiple platforms, maintains and controls the liquid level while meeting all design specifications, including time constant, no overshoot, less settling, and rise time. For research simulation work, MATLAB software's FOMCON toolbox is utilised.

Exploring the Potential of 3D Printing Technology for Sustainable Plastic Roads: A Preliminary Investigation

The urgency of climate change has highlighted the need for sustainable road construction materials, replacing the conventional asphalt, which significantly contributes to global warming and the urban heat island effect. With this in mind, the construction of the world’s first 30-m plastic road in Zwolle, Netherlands, in 2018, opened the door for novel plastic applications as paving materials. However, its application is currently still limited to sidewalks and light-load cycling lanes. The feasibility of utilizing 3D printing technology to provide the necessary structural design flexibility for the production of plastic pavement modules that can withstand heavy traffic and extreme weather conditions was examined in this preliminary study. The suitability of six plastic materials (PLA, PETG, ABS, TPU, Nylon, and polycarbonate) for 3D printing was evaluated. Polylactic acid (PLA), and polyethylene terephthalate glycol (PETG) were identified as the most suitable materials for this study. Three small-scale structural systems, namely hollow modular with plastic columns, hollow modular with solid plastic cones, and hollow modular with X-bracing, were designed and successfully printed using the adopted materials and a 3D printer. The developed systems were subsequently subjected to compression testing to assess their structural performance under heavy traffic loads and demonstrate the feasibility of the concept. The results showed that the PLA conic structural system was effective and exhibited the highest compression strength, while the PETG conic system exhibited ductile behavior with superior thermal stability. The study suggests that the hybrid system of PLA and PETG materials may improve the overall performance, combine flexibility and strength, and potentially improve the resistance to extreme weather and heavy traffic. These findings prove that 3D printing technology has the potential to revolutionize the road construction industry and provide more sustainable solutions for infrastructure development.

Gas concentration in rarefied flows: Experiments and modeling

The relationship between gas-surface scattering dynamics and flow through conical systems in the rarefied regime has been explored with experimental and computational tools. Molecular beam-surface scattering experiments were used to characterize the inelastic scattering dynamics of Ar and N2 on a highly oriented pyrolytic graphite (HOPG) surface. These data were then used to develop a gas-surface scattering approach for kinetic fluid simulations, which combines the diffuse scattering and Cercignani-Lampis-Lord (CLL) models. The translational energy and angular flux distributions from the beam-surface scattering experiments were used to obtain the normal energy accommodation (αn) parameter as well as the effective surface mass (M) in the CLL model. Constant values of αn=0.9, M = 40 amu for Ar and αn=0.75, M = 28 amu for N2 were found to capture the experimental angular flux scattering distributions over a wide range of incident energies and angles. The gas-surface model was subsequently used in direct simulation Monte Carlo (DSMC) simulations of the flux of directed gas flow through a conical concentrator and compared with measurements of gas concentration with a prototype concentrator in separate molecular beam experiments. Comparisons of predicted concentration pressure ratios (pressure in an accommodation chamber with vs. without concentrator) with measured values for three free-stream velocities of Ar and N2 showed maximum deviations of 4.8% and 9.8% for Ar and N2, respectively. The simulations show that gas-surface collisions resulting in the loss of the normal component of the incident energy while preserving the tangential momentum of the impinging atom or molecule, resulting in super-specular scattering, lead to higher concentration of gases than purely specular, energy conserving gas-surface interactions. For conical concentrators, with inlet-to-outlet area ratios of 133 and 600, specular reflections result in concentration factors (flux through an orifice with vs. without concentrator) of only ∼8, while super-specular scattering results in concentration factors of 64 and 127, respectively.

Null-forms of conic systems in R3 are determined by their symmetries

We address the problem of characterisation of null-forms of conic 3-dimensional systems, that is, control-affine systems whose field of admissible velocities forms a conic (without parameters) in the tangent space. Those systems have been previously identified as the simplest control systems under a conic nonholonomic constraint or as systems of zero curvature. In this work, we propose a direct characterisation of null-forms of conic systems among all control-affine systems by studying the Lie algebra of infinitesimal symmetries. Namely, we show that the Lie algebra of infinitesimal symmetries characterises uniquely null-forms of conic systems.

Axial displacement of the suprastructures at the conical implant — abutment interface

BACKGROUND: The inconsistency of the congruence of the surface of the implantabutment interface leads to the impaired communication of the implant shaft with the oral cavity, breakdown of the structure, including the implant, and changes in the occlusal relationships because of axial displacement.
 AIM: This study aimed to investigate the degree of axial displacement of abutments made relative to implants and analogs. Specific tasks were as follows: (1) to make various abutments for implants with a conical connection obtained from MIS, (2) to study the value of axial displacement of abutments of each type relative to the implant with load modeling, and (3) to examine the value of the axial displacement of abutments of each type relative to the analog of the implant from the tightening force of the screw.
 MATERIALS AND METHODS: Axial displacements were tested using implants and analogs of MIS implants with conical joints. Original and non-original abutments were chosen as suprastructures. The original abutment was presented by CS-CPK62. Abutments for the conical connection C1 were made by milling, laser sintering, and casting according to burned models. The fastening of implant analogs and implants was made in a block of plaster of the 4th class. The study was conducted in a simulation complex we have developed, which creates a cyclic load within 30 kg. The study was divided into two stages. In the first stage, axial displacements on analogs from the force of screw tightening were examined. Abutments were attached with various forces: 7 Ncm (tightening force with a simple screwdriver), 15 Ncm, and 30 Ncm. After each screw tightening, vertical measurements were made with a micrometer. In the second stage, axial displacements on implants under load in the original simulation complex were assessed. The screw was tightened with a force of 30 Ncm, as recommended by the manufacturer, and load simulation was performed. Measurements were made both before and after the load simulation.
 RESULTS: The original abutments and those made by milling showed the greatest deviation (0.056 mm and 0.066 mm, respectively), and abutments obtained by casting had deviations of 0.047 mm. The smallest deviation was found in the abutment made by laser sintering (0.032 mm). The values obtained in the second stage were as follows. Original abutments and abutments obtained by milling showed the smallest axial displacement when modeling the load (0.00167 mm each). Moreover, the abutments obtained by casting and laser melting showed significant displacements (0.007 mm and 0.004 mm, respectively).
 CONCLUSIONS: A pattern was revealed: the smoother the surface of the conical parts, the stronger the axial displacement on the analog implants in the range of 730 Ncm, whereas an uneven surface gives the smallest axial displacement, and fixation according to the protocol provided resistance to chewing loads on the implants in the original and milled abutments. The use of a platform with a conical system to create high-precision orthopedic structures has certain limitations because an error in the height of the restoration is created in laboratory conditions. The use of non-original suprastructures leads to the accumulation of errors. Thus, it is necessary to further evaluate conical systems from other manufacturers and improve the accuracy of restorations based on dental implants.

Stabilization of Robot-Environment Interaction Through Generalized Scattering Techniques

A control design framework for the coupled stability problem in robotics is presented. The proposed framework fundamentally generalizes the conventional passivity-based approaches to the coupled stability problem. In particular, it allows for stabilization of not necessarily passive robot-environment interaction where both the manipulator and the environment are dissipative systems with quadratic supply rates. In contrast with existing results, the proposed framework can be used in combination with an arbitrary robot’s tracking control algorithm, and its stabilizing action when in contact with environment does not affect the robot’s trajectory tracking performance in free space. The framework is based on the recently developed nonplanar conic systems formalism and generalized scattering-based stabilization methods. A detailed design example is presented which illustrates the capabilities of the proposed method.

TE-GDQE implementation to investigate the vibration of FG composite conical shells considering a frequency controller solid ring

This article investigates the free vibration response of a conical system supported by an intermediate solid ring. The ingredients of the shell are considered a polymer reinforced with graphene platelets (GPLs). The distribution of GPLs is assumed to be uniform, and their orientation is considered random in each layer of the composite. The variation of GPL weight fraction within layers is based on the functionally graded patterns. Effective material properties are calculated utilizing the Halpin–Tsai homogenization procedure. The fundamental formulation of the shell is founded by the first-order shear deformation theory and Donnell’s kinematic assumptions. The motion equations and associated boundary and compatibility conditions are derived by Hamilton’s principle. Solving the governing equations due to the existence of a solid frequency control ring is not possible using conventional numerical methods. For this reason, a new type of GDQ method is applied, which is a combination of this technique with a finite element procedure (GDQE). By combining this method with the method of trigonometric expansion (TE) analysis, the equations of motion of the structure are solved. After illustrating the validation studies, parametric examples are given to investigate the effect of material properties, boundary conditions, and ring position on the shell frequencies.

Projection and Rescaling Algorithm for Finding Maximum Support Solutions to Polyhedral Conic Systems

We propose a simple projection and rescaling algorithm that finds maximum support solutions to the pair of feasibility problems: [Formula: see text] where L is a linear subspace in [Formula: see text] and [Formula: see text] is its orthogonal complement. The algorithm complements a basic procedure that involves only projections onto L and [Formula: see text] with a periodic rescaling step. The number of rescaling steps and, thus, overall computational work performed by the algorithm are bounded above in terms of a condition measure of the above pair of problems. Our algorithm is a natural but significant extension of a previous projection and rescaling algorithm that finds a solution to the full support problem: [Formula: see text] when this problem is feasible. As a byproduct of our new developments, we obtain a sharper analysis of the projection and rescaling algorithm in the latter special case.

Null-Forms of Conic Systems in ℝ3 are Determined by Their Symmetries

Null-Forms of Conic Systems in ℝ3 are Determined by Their Symmetries

Spatial Rigid-Flexible-Liquid Coupling Dynamics of Towed System Analyzed by a Hamiltonian Finite Element Method

An effective Hamiltonian finite element method is presented in this paper to investigate the three-dimensional dynamic responses of a towed cable-payload system with large deformation. The dynamics of a flexible towed system moving in a medium is a classical and complex rigid-flexible-liquid coupling problem. The dynamic governing equation is derived from the Hamiltonian system and built-in canonical form. A Symplectic algorithm is built to analyze the canonical equations numerically. Logarithmic strain is applied to estimate the large deformation effect and the system stiffness matrix will be updated for each calculation time step. A direct integral solution of the medium drag effect is derived in which the traditional coordinate transformation is avoided. A conical pendulum system and a 180° U-turn towed cable system are conducted and the results are compared with those retraced from the existing Hamiltonian method based on small deformation theory and the dynamic software of Livermore software technology corp. (LS-DYNA). Furthermore, a circularly towed system is analyzed and compared with experimental data. The comparisons show that the presented method is more accurate than the existing Hamiltonian method when large deformation occurred in the towed cable due to the application of logarithmic strain. Furthermore, it is more effective than LS-DYNA to treat the rigid-flexible-liquid coupling problems in the costs of CPU time.

Large Deformation Dynamic Analysis of a Cable System by a New Hamiltonian Finite Element Method

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.

Combinatorial invariants for nets of conics in mathrm {PG}(2,q)

The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics over {mathbb {C}} and mathbb {R} in 1906–1907. The analogous problem for finite fields mathbb {F}_q with q odd was solved by Dickson in 1908. In 1914, Wilson attempted to classify nets (two-dimensional systems) of conics over finite fields of odd characteristic, but his classification was incomplete and contained some inaccuracies. In a recent article, we completed Wilson’s classification (for q odd) of nets of rank one, namely those containing a repeated line. The aim of the present paper is to introduce and calculate certain combinatorial invariants of these nets, which we expect will be of use in various applications. Our approach is geometric in the sense that we view a net of rank one as a plane in mathrm {PG}(5,q), q odd, that meets the quadric Veronesean in at least one point; two such nets are then equivalent if and only if the corresponding planes belong to the same orbit under the induced action of mathrm {PGL}(3,q) viewed as a subgroup of mathrm {PGL}(6,q). Since q is odd, the orbits of lines in mathrm {PG}(5,q) under this action correspond to the aforementioned pencils of conics in mathrm {PG}(2,q). The main contribution of this paper is to determine the line-orbit distribution of a plane pi corresponding to a net of rank one, namely, the number of lines in pi belonging to each line orbit. It turns out that this list of invariants completely determines the orbit of pi , and we will use this fact in forthcoming work to develop an efficient algorithm for calculating the orbit of a given net of rank one. As a more immediate application, we also determine the stabilisers of nets of rank one in mathrm {PGL}(3,q), and hence the orbit sizes.

Design of Microelectronics Microsystem Neural Learning Controller Based on Subspace State Recognition

Aiming at the large delay and large inertia in cone storage and irrigation, this paper adopts machine learning and predictive control, proposes a closed-loop N4SID (numerical subspace state system identification) algorithm, which is adjusted by IMC based on Smith predictor PI controller and parameter tuning are given, and the steps designed in cascade control are given. The experimental results verify the effectiveness of the proposed method.Compared with closed-loop SVA and open-loop methods, the method proposed in this paper has better verification results and pole assignment. According to this model, the PI controller is adjusted using IMC based on Smith Smith predictor. Compared with the traditional ZN adjustment method, this method shows good results in a conical system. In addition, the PI parameters can be adjusted to obtain robust control using the H∞-based mixed sensitivity algorithm. The contribution of this paper is the use of closed subspace system identification to identify the MIMO state space. The developed model validates the IMC tuned PI controller based on the Smith predictor in the factory.

Prosthodontics Using Removable Platform Switching Technologies (Multiunit, On1) as Exemplified by Conical Connection Implant Systems for Early and Immediate Loading.

The removable platform switching technology (multiunit, Оn1) was tested intraoperatively using the passive placement technique as exemplified by a conical connection implant system, which makes it possible to visually control the placement of these platforms with respect to the alveolar bone in the correct orthopedic position. The technology is characterized by a rapid epithelialization of tissues around the base platform until the final integration of the implant, minimal trauma in the emergence profile zone, and an improved minimally invasive orthopedic protocol for working on a removable platform switching base.

Analytical Study of Non-Recessed Conical Hole Entry Hybrid/Hydrostatic Journal Bearing with Constant Flow Valve Restrictor

The present work studies the analysis of a non recessed hole entry conical hybrid/hydrostatic journal bearing adjusted for constant flow valve (CFV) restriction. The paper provides effectiveness between the conical bearings with hole entry operating in hybrid and hydrostatic mode. The Reynolds formulae, for the flow of fluid through the mating surfaces of a conical journal and bearing, are numerically worked out in both the modes considering the finite element analysis (FEA) and the necessary boundary preconditions. Holes in double row are marked on conical bearing circumference to accommodate the CFV restrictors, the angular distance between two holes are 30o apart from the apex. Qualitative features of the conical journal bearing system with hole entry have been elaborated to analyze bearing performance for radial load variation Wr = 0.25-2. Numerical results obtained from the present study indicate that load carrying capacity of conical bearing, operating in hydrostatic mode, is enhanced by the maximum pressure, direct fluid film damping and direct film stiffness coefficients vis-a-vis corresponding hybrid mode. 

Refining the partition for multifold conic optimization problems

ABSTRACT In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramírez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2–30):205–227] for conic optimization problems, and in Peña and Roshchina [A complementarity partition theorem for multifold conic systems, Math Program. 2013;142(1–2):579–589] for homogeneous feasibility problems. We show that both can be treated within the same unified geometric framework and extend the latter notion to optimization problems. We also show that the two partitions do not coincide, and their intersection gives a seven-set index partition. Finally, we demonstrate that the partitions are preserved under the application of nonsingular linear transformations, and in particular, that a standard conversion of a second-order cone program into a semidefinite programming problem preserves the partitions.

Transitions between phyllotactic lattice states in curved geometries

Phyllotaxis, the regular arrangement of leaves or other lateral organs in plants including pineapples, sunflowers and some cacti, has attracted scientific interest for centuries. More recently there has been interest in phyllotaxis within physical systems, especially for cylindrical geometry. In this letter, we expand from a cylindrical geometry and investigate transitions between phyllotactic states of soft vortex matter confined to a conical frustum. We show that the ground states of this system are consistent with previous results for cylindrical confinement and discuss the resulting defect structures at the transitions. We then eliminate these defects from the system by introducing a density gradient to create a configuration in a single state. The nature of the density gradient limits this approach to a small parameter range on the conical system. We therefore seek a new surface, the horn, for which a defect-free state can be maintained for a larger range of parameters.

New design modifications of the supporting ring for a large deployable space reflector

Though theoretical and experimental studies of the design of large deployable antenna reflectors have already been carried out for quite a long time, the results obtained in this area of research still attract a lively interest and have good application prospects. In the present paper, two novel design modifications are described for the symmetric (i.e. with circular apertures) radio telescopes. The novelty consists in that improved stiffness and stability have been obtained by combining two conical pantograph systems and thus getting the whole hinged-bar structure consisting of cylindrical and sliding hinges only. Three FE models of the supporting ring structure are constructed and compared with one another using the NASTRAN FEA software. The degrees of freedom of hinges are simulated in local coordinate systems. A static, modal and buckling analysis had been done to investigate, strength and stiffness characteristics.

Nets of conics of rank one in $$\mathrm {PG}(2,q)$$, q odd

We classify nets of conics of rank one in Desarguesian projective planes over finite fields of odd order, namely, two-dimensional linear systems of conics containing a repeated line. Our proof is geometric in the sense that we solve the equivalent problem of classifying the orbits of planes in $$\mathrm {PG}(5,q)$$ which meet the quadric Veronesean in at least one point, under the action of $$\mathrm {PGL}(3,q) \leqslant \mathrm {PGL}(6,q)$$ (for q odd). Our results complete a partial classification of nets of conics of rank one obtained by Wilson (Am J Math 36:187–210, 1914).

Development of a New Drill Design to Improve the Temperature Control during the Osteotomy for Dental Implants: A Comparative In Vitro Analysis

The present in vitro study evaluated a new drill design to improve the temperature control during the osteotomies for dental implant installation, comparing with two drill designs that use conventional external irrigation. Three blocks of synthetic cortical bone were used for osteotomy procedures. Three groups were created: control group 1 (Con1), where a conical multiple drill system with a conventional external irrigation system was used; control group 2 (Con2), where a single bur with a conventional external irrigation system was used; and, test group (Test), where the new single bur (turbo drill) with a new irrigation system was used. Twenty osteotomies were made without irrigation and with intense irrigation, for each group. A thermocouple was used to measure the temperature produced during the osteotomies. The measured temperature were: 28.9 ± 1.68 °C for group Con1; 27.5 ± 1.32 °C for group Con2; 26.3 ± 1.28 °C for group Test. Whereas, the measured temperatures with irrigation were: 23.1 ± 1.27 °C for group Con1; 21.7 ± 1.36 °C for group Con2; 19.4 ± 1.29 °C for group Test. The single drill with a new design for improving the irrigation and temperature control, in comparison with the drill designs with conventional external irrigation.