Spiral Point Research Articles

Auto-resonance process under the interaction of solitons with external force and dissipation

Algebraic soliton interactions with an external force in the presence of Reynolds viscosity is investigated. In the absence of an external force, the soliton amplitude decays over time. However, when an external force is introduced, it acts as a restoring force, and in some cases, the soliton’s amplitude is preserved. A dynamical system that governs the soliton amplitude and its crest position is obtained assuming a weak force and weak viscosity. For an external force with a Gaussian shape, the dynamical system has two equilibrium points, namely, a saddle and a stable spiral. Asymptotic results are compared with direct numerical simulations, and a strong qualitative agreement is observed. The stable spiral predicted by the asymptotic theory is stable in the sense that soliton solutions with a chosen amplitude and crest position near the spiral point are attracted to it, preserving their amplitude and location.

Dynamics of 2 × 2 matrix non-Hermitian quantum systems on Bloch sphere

By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely, the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken PT non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point (EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.

Diagnosing of Parkinson's disease based on hand drawing analysis using Bi‐Directional LSTM equipped with fuzzy inferential soft‐max classifier

AbstractParkinson's Disease (PD) is a brain‐related disease that eventually causes disability and disrupts a person's normal life. Most physicians and researchers try to diagnose it quickly and treat it on time. In recent years, computer science and the field of artificial intelligence (machine learning) have helped researchers find a way to detect the disease early. This article proposes a method that diagnoses Parkinson's disease by analyzing the hand drawing shaped by the individuals using Bi‐Directional Long Short‐Term Memory (Bi‐LSTM) neural network. In addition, this paper proposes a Fuzzy Inferential Classifier for the Dense layer, which classifies the output of LSTM Blocks to the associated classes by modifying the Soft‐max function. Our decision to propose this classifier was because, in some cases, hand‐drawing data related to people with Parkinson's disease have no significant difference with the healthy subjects for the distinguishing and are often very similar to each other. A standard dataset has been used in this paper, which includes spirals drawn test (including static spiral, dynamic spiral, and stability specific point) by a group of healthy people and people with Parkinson's disease. The proposed method has reached 97%, 98.5%, and 100% accuracy rates for the three mentioned spiral tests with a smoother training loss and accuracy plots. In addition, the results outperform state‐of‐the‐art research conducted on this dataset and show at least more than 2.5% improvement in the accuracy rate in comparison.

Three-dimensional critical points and flow patterns in pulmonary alveoli with rhythmic wall motion

The dynamics of airflow in the pulmonary acini are of broad interest in understanding respiratory diseases and the fate of inhaled particles. This study investigates the three-dimensional (3d) alveolar flows with rhythmic cavity wall motion, using a finite element method based computational fluid dynamics. This study reports the new research findings on the critical points and associated flow patterns. The locations of critical points are found based on the Brouwer degree theory and Broyden’s method. The phase portrait is used to evaluate the flow patterns around the critical points and the stability (repelling/attracting property) of the critical points on the symmetry plane of the alveolus. Based on the Poincare–Bendixson theorem, the closed orbits on the symmetry plane are found which have the capability to alter the spiral direction of the spiral streamlines. In the 3d space, the alveolar flow is symmetric about the geometric symmetry plane of the alveolus. Different types of 3d critical points, including saddle, spiral, and spiral saddle, are revealed. There are only one saddle point and at least one spiral point or spiral saddle in the alveolar flow. Spiral points and spiral saddles are located on the vortex core line and their number is dependent on the Reynolds number and varies with time. The study of critical points and their evolution helps us to understand the mechanism of irreversible transport of particle tracers from a new perspective.

Global stability and bifurcation of macroscopic traffic flow models for upslope and downslope

A macro-continuum model of the traffic flow is derived from a micro-car-following model that considers both the upslope and downslope by using the transformation relationship between macro- and micro-variables. The perturbation propagation characteristics and stability conditions of the macroscopic continuum equation are discussed. For uniform flow in the initial equilibrium state, the stability conditions reveal that as the slope angle increased under the action of a small disturbance, the upslope stability increases and downslope stability decreases. Moreover, under a large disturbance, the global stability analysis is carried out by using the wavefront expansion technique for uniform flow in the initial equilibrium state. For the initial nonuniform flow, nonlinear bifurcation analysis such as Hopf bifurcation and saddle–node bifurcation is carried out at the equilibrium point. Subcritical Hopf bifurcation exists when the traffic flow state changes; thus, the limit cycle formed by the Hopf bifurcation is unstable. And the existence condition of saddle-node bifurcation is obtained. Simulation results verify the stability conditions of the model and determine the critical density range. The numerical simulation results show the existence of Hopf bifurcation in phase space, and the spiral saddle point of saddle-node bifurcation varies with the slope angle. Furthermore, the impact of the angle of both the upslope and downslope on the evolution of density waves is investigated.

Special Spirals are Produced by the ROTASE Galactic Spiral Equations with the Sequential Prime Numbers

In this paper, the sequential prime numbers are used as variables for the galactic spiral equations which were developed from the ROTASE model. Special spiral patterns are produced when prime numbers are treated with the unit of radian. The special spiral patterns produced with the first 1000 prime numbers have 20 spirals arranged in two groups. The two groups have perfect central symmetry with each other and are separated with two spiral gaps. The special spiral pattern produced with natural numbers from 1 to 7919 shows 6 spirals in the central area and 44 spirals in the outer area. The whole 7919 spiral points can be plotted with either 6-spiral pattern or 44-spiral pattern. The special spiral pattern is well explained with careful analysis, it is concluded that all prime numbers greater than 3 must meet one of the equations: P1 = 1 + 6 * n (n > 0, n is an integer) P5 = 5 + 6 * m (m ≥ 0, m is an integer) Matching one of the equations is a necessary condition for a number to be a prime number, not a sufficient condition. Twin prime numbers can only be formed between P1 and P5 prime numbers, n must be 1 greater than m. The largest prime number is known at the moment 2^(82,589,933) – 1 is a P1 prime number.

Interval Type-2 Fuzzy Differential Equations and Stability

This article is devoted to present a framework for studying type-2 fuzzy calculus. Some new concepts pertaining to interval type-2 fuzzy functions (IT2FF) and interval type-2 fuzzy differential equations (IT2FDE) with their stability analysis are introduced. A new definition of type-2 fuzzy derivative called type-2 granular derivative (T2gr-derivative) is defined to overcome the disadvantages of the previous definitions of type-2 fuzzy derivatives. Furthermore, the definitions of elementary arithmetic on the set of interval type-2 fuzzy numbers (IT2FNs) and the set of interval type-2 fuzzy complex numbers are presented. The notion of granular metric on the set of IT2FNs is also defined. Besides, the concepts of continuity, integral, and limit of IT2FFs are introduced. Using the concept of type-2 granular fuzzy Laplace transform and the approximations of T2gr-derivative proposed in this article, the exact and approximate solutions of interval T2FDE are presented. Then, some new concepts such as fuzzy node, fuzzy saddle spiral point, fuzzy star, and so forth lay the groundwork for the analysis of interval T2FDE stability. Several examples are given to illustrate the presented notions.

ISSM-ELM - a guide star selection for a small-FOV star sensor based on the improved SSM and extreme learning machine.

The construction of a guide star catalog is crucial for a star sensor to achieve accurate star map recognition and attitude determination. At present, the methods of a guide star catalog for a large field of view (FOV) star sensor have been relatively mature. However, for a small-FOV star sensor, there are still certain problems, such as a large storage capacity of a guide star catalog, uneven distribution of stars, and easy occurrence of voids. To address these problems, we propose a construction method of a small-FOV star sensor guide star catalog based on the combination of the improved spherical spiral method (ISSM) and extreme learning machine (ELM) named the ISSM-ELM. First, a spiral reference point is used as an optical axis pointing of the star sensor, and the guide stars are preliminarily screened based on the star-diagonal distance between the star and the reference point, and the star-density and magnitude characteristics of the guide star. Then the ELM is used to supplement the guide star empty sky area to construct an integrity guide star catalog. The experimental results demonstrate that the proposed method can reduce the storage capacity of the guide star catalog, and improve its uniformity, integrity, and average brightness.

Construction of the Guide Star Catalog for Double Fine Guidance Sensors Based on SSBK Clustering.

In the Chinese Survey Space Telescope (CSST), the Fine Guidance Sensor (FGS) is required to provide high-precision attitude information of the space telescope. The fine star guide catalog is an essential part of the FGS. It is not only the basis for star identification and attitude determination but also the key to determining the absolute attitude of the space telescope. However, the capacity and uniformity of the fine guide star catalog will affect the performance of the FGS. To build a guide star catalog with uniform distribution of guide stars and catalog capacity that is as small as possible, and to effectively improve the speed of star identification and the accuracy of attitude determination, the spherical spiral binary K-means clustering algorithm (SSBK) is proposed. Based on the selection criteria, firstly, the spherical spiral reference point method is used for global uniform division, and then, the K-means clustering algorithm in machine learning is introduced to divide the stars into several disjoint subsets through the use of angular distance and dichotomy so that the guide stars are uniformly distributed. We assume that the field of view (FOV) is 0.2° × 0.2°, the magnitude range is 9∼15 mag, and the threshold for the number of stars (NOS) in the FOV is 9. The simulation shows that compared with the magnitude filtering method (MFM) and the spherical spiral reference point brightness optimization algorithm (SSRP), the guide star catalog based on the SSBK algorithm has the lowest standard deviation of the NOS in the FOV, and the probability of 5∼15 stars is the highest (over 99.4%), which can ensure a higher identification probability and attitude determination accuracy.

3D Reconnection Geometries With Magnetic Nulls: Multispacecraft Observations and Reconstructions

AbstractMagnetic reconnection is universal in various plasma environments like the solar atmosphere, planetary magnetosphere, and laboratory to trigger explosive phenomena. Its nature and magnetic structure in two dimensions (2D) have been abundantly analyzed. The three‐dimensional (3D) characteristics of reconnection are different from 2D, and the mysteries of its 3D geometry are under exploration. A critical character in 3D is the presence of magnetic nulls, which is essential when the magnetic field topology is changing. The four identical spacecraft from the Cluster mission enable several methods for analyzing and visualizing the 3D nature of the magnetic structure. In this paper, we focus on reviewing the magnetic topology of the reconnection geometry containing 3D magnetic null points. Applying the fitting‐reconstruction method to Cluster data, magnetic null pairs or multiple magnetic nulls linked by separators or helically wrapped spines are found in the reconnection diffusion region and turbulent outflow region. The reconstructed magnetic structures show that the 2D features are parts of local approximations of the 3D geometries. The 2D regimes of antiparallel and component reconnection can simultaneously occur in 3D separator reconnection. The flux ropes are formed along the spine line or in a region enclosed by wrapped fan surfaces in the presence of spiral null points.

Оценка состояния пилота по данным видеоокулографии и параметрам альфа-ритмов головного мозга путем моделирования его нейронной активности

The H.R. Wilson and J.D. Cowan model of human brain neural activity is considered, which connects the latent (non-measurable) parameters of external excitation with the brain neuronal activity parameters which are available for observation, with alpha rhythm frequencies being in use in this capacity. By means of computational experiments, revealed are the ranges of latent parameters, which ensure the occurrence of the Poincaré—Andronov—Hopf bifurcation (transforming the spiral sink to the spiral source equilibrium point with a limit cycle, or vice versa) that leads, in the first approximation, to the appearance of alpha rhythms. Relative changes of the latent parameters representing external excitation are estimated through the primary indices of oculomotor activity (gaze movement entropies and gaze fixation durations), which makes it possible to assess the pilot proximity to falling into a low efficiency state, including the real time mode.

An appraisal of the cradle-to-gate energy demand and carbon footprint of high-speed steel cutting tools

The awareness of the environmental impact of the manufacturing sector has increased over the last few decades. This paper presents the results of an LCA-based approach used to evaluate the production of a threading tool (i.e., an M10 × 1.25 spiral point tap) made of high-speed steel. The cumulative energy demand and CO2-equivalent emissions have been quantified throughout the entire tool manufacturing process. Both the pre-manufacturing steps and the upstream/downstream flows of the used material have been accounted for, considering cradle-to-gate (plus end-of-life) system boundaries. The results show that the share of primary energy employed to produce the tool is mainly imputable to the manufacturing processes. Therefore, this analysis could contribute to fostering the development of structured assessment frameworks that would allow cutting tool manufacturers to identify the weak points of their production routes to be optimized.

Effect of predators' behavior on prey-predator interaction

In this paper, we study the effect of the behavior of predators on prey-predator interaction. We assume that there is one prey population that suffers from the fear of predators which could force it to move in to the refuge; and three are two predator populations, one of them is aggressive in its attack and the other one using sit-and-wait procedure, which is less aggressive. All the model’s equilibrium points have been found and their stability was established. The possibility of transcritical and Hopf bifurcation was also investigated and numerical simulations were given. The effect of prey refuge and fear also are detected. The cost of them is to allow the model to reach to double transcritical point. The effect of the competition between prey populations is to convert the model from the stable limit cycle to a spiral stable equilibrium point of afraid prey with predator. When it becomes large it converts the model to the stable trivial solution.

Effects of vortex dynamics mechanism of blade-end treatment on the flow losses in a compressor cascade at critical condition

Elucidating the underlying mechanism of the vortex dynamics in compressors is essential for determining the sources of the flow losses in compressor cascades. Hence, the effects of blade-end treatments on a linear compressor cascade should be analyzed at the microscale. In this study, the design parameters for various blade-end treatment methods were determined based on the topological structure of the saddle and spiral points on the blade surface. Then, based on the results, the underlying mechanism of the corresponding vortex dynamics was determined. The results showed that the total flow loss is primarily determined by the passage and concerted shedding vortices and the profile losses. The positive effect of the blade-end treatment is that it weakens the vortex structures, while its negative effect is that it causes the low-energy fluid clusters to converge into a separation bubble. However, the negative effects are compensated for by the positive, resulting in a significant reduction in the total flow loss. Furthermore, the changes induced in the pressure gradients by the treatments were also analyzed in this study. Thus, the microscale relationship between the vortex structure and the flow loss was clarified and the suitability of various blade-end treatment for preventing cascaded flow losses was analyzed in this study.

The effect of polishing protocol on surface gloss of different restorative resin composites

Aim The purpose of this in vitro study was to determine the effects of different polishing protocols on the surface gloss (SG) of different commercial dental resin composites (RCs). Material and methods A total of 147 block-shaped specimens (40 mm length × 10 mm width × 2 mm thick) were made from conventional RCs (G-aenial Ant. and Flo X), bulk-fill RC (Filtek Bulk Fill), fluoride-releasing RCs (BEAUTIFIL II, ACTIVA-Restorative) and discontinuous microfiber-reinforced RCs (Alert and everX Flow). Each group was subdivided into seven subgroups (n = 3), according to polishing protocol: Laboratory-machine polishing with different siliconcarbide paper grits (G1: 320) → (G2: 800) → (G3: 1200) → (G4: 2000) → (G5: 4000). Chairside-hand polishing using a series of Sof-Lex spiral (G6) and abrasive polishing points (G7). Glossmeter was used to determine the SG at 60° incidence angle. SG was measured before and after polishing. Three-dimensional (3 D) noncontact optical profilometer and scanning electron microscopy (SEM) analysis were performed. Data were analyzed using ANOVA (p = .05). Results Significant differences in SG (ranged 3–93 GU) were found according to the type of polishing protocol and RC (p < .05). Specimens polished with 4000 grit paper showed the highest SG (93 GU) values among all the groups tested. Conclusions The tested chairside-hand polishing protocols presented lower SG values than laboratory-machine polishing (4000 silicon paper grit) and unpolished surfaces.

Spiral Dynamics, System Cycles and New Organizational Models: Pearlescent Enterprises

According to C. Graves, D. Beck, and C. Cowan’s Spiral Dynamics theory, the development of a socio-economic system, including an individual, organization, society, occurs discretely by moving from one level to another under the influence of change in the dominant value system. The authors of the Spiral Dynamics theory point to 8 levels, marked with a uniform color — from beige to turquoise. In this article, based on the analysis of trends in enterprises’ organizational models, the list of known organizational forms is supplemented by a new model — “pearlescent organization”. This form of an organization aims to strengthen employees’ emotional attachment due to an increase in the enterprise’s internal diversity, adaptability, and flexibility of the structure. The model of synthesis of the theory of linear change of value systems and cyclical change of four phases of the enterprise’s state is also developed in the article. Each of these stages is characterized by the dominance of the object, project, process, or environmental subsystems of the enterprise. The conditions for the transition from one stage of enterprise development to another, particularly the transformation of the turquoise stage into the pearlescent one, are shown based on this model.

Effects of Different Polishing Protocols and Curing Time on Surface Properties of a Bulk-fill Composite Resin.

To determine the effects of different polishing protocols and curing times on the surface roughness (SR), surface gloss (SG) and surface hardness (SH) of a bulk-fill composite resin (BCR). A total of 30 block-shaped specimens (40 mm long × 10 mm wide × 2 mm thick) were made from Filtek Bulk-Fill composite resin and divided into two groups (n = 15) according to curing time (10 and 40 seconds). Each group was subdivided into five groups (n = 3) according to the polishing protocol: laboratory polishing with different silicon paper grits (G1:1200) → (G2:2400) → (G3:4000). Chairside polishing was performed using a series of Sof-Lex spiral (G4) and Jiffy Polisher (G5) points. The SR was measured by a surface profilometer. A Vickers indenter was used to test the SH, and a glossmeter was used to determine the SG at 60 degrees. The SR, SG and SH were quantified before and after polishing. A scanning electron microscopy (SEM) evaluation was then performed. The curing time did not affect the surface properties of the BCR (P > 0.05). Significant differences in SR (ranging from 0.1 to 2 μm) and SG (ranging from 20 to 90 GU [gloss unit]) were found according to the type of polishing protocol (P < 0.05). The SH values following different polishing protocols were significantly higher (ranging from 82 to 95 VH [Vickers hardness]) than the polishing values obtained before the polishing protocols (P < 0.05). The tested chairside polishing protocols presented lower SG and higher SR values than the laboratory polishing protocols.

Symmetric periodic orbits in the Moulton–Copenhagen problem

We consider the planar restricted four-body problem proposed by Moulton. One infinitesimal mass moves under the attraction of three mass points in collinear Euler’s configuration, namely $$P_0 (m_0 = \mu \,m)$$ is placed at the origin, and other two identical points $$P_1 (m)$$ and $$P_2 (m)$$ are placed at the same distance from the origin. The problem is an extension of the well-known Copenhagen problem, in which $$P_0$$ does not exist, and therefore, the name is chosen for the considered problem. We perform a study on the evolution of families of symmetric periodic orbits (characteristic curves) as the mass parameter $$\mu $$ evolves. Compared with the Copenhagen problem, we find new families of periodic orbits and how the classical ones change. We also analyse the number and evolution of spiral points, which represent the heteroclinic orbits connecting equilibrium points.

The First Solar Flare Effect Observation at UiTM-SID Station during Solar Cycle 23-24

International Heliophysical Year (IHY; 2007-2009) has a remarkable impact on space and earth electromagnetism research and society. For Malaysian perspectives, it acts as a spiral point to the expanding of space weather-related research. The research activities involve installation of real-time Magnetic Data Acquisition System of Circum-pan Pacific Magnetometer Network, i.e. MAGDAS/CPMN for space weather study and application, which was deployed for the IHY; 2007-2009. In addition to MAGDAS system, to understand the characteristics of the lower ionospheric layer (60-150km) during space weather events, a Very Low Frequency (VLF) monitoring system has been developed. The MAGDAS and VLF monitoring system called UiTM-SID are located at Universiti Pendidikan Sultan Idris, UPSI (3.71’, 101.53’), Malaysia. The first observation effects of solar flare during November 2016 to March 2017, for the period of a minimum solar cycle 23-24 have been examined on sub-ionospheric VLF signals from VTX4 (19.2 kHz) and NWC (19.8 kHz) transmitter monitored at UPSI. In general, the level of amplitude reading for VTX4 signals is higher than NWC signals for quite diurnal variations. The effects of the solar flare class C7.5 on 29th November 2016 shows an enhancement of amplitude due to increase in the lower region electron density by the radiation of solar flare. The average daily amplitude reading was compared to the average value of solar flare event, the result shows the percentage difference is 12% increased in VTX4 and NWC signals.

A novel polyvinyl alcohol and hypromellose gap-coated humidity sensor based on a Mach–Zehnder interferometer with off-axis spiral deformation

A novel humidity sensor based on a Mach–Zehnder interferometer (MZI) in normal single-mode fiber (SMF) was developed and investigated. The MZI is composed of a polyvinyl alcohol coated gap that serves as a sensitive beam splitter at the input end of the MZI and an off-axis spiral deformation point that acts as a beam combiner at the output end of the MZI. The coated gap is formed between the end faces of 2 SMFs, where the humidity-sensitive polyvinyl alcohol and hypromellose film is deposited on the end face of the input SMF. The off-axis spiral deformation is achieved by twisting the lead-out fiber under continuous arc discharging with the appropriate off-axis radius. When the humidity of the external environment changes, both the refractive index and the thickness of the hygroscopic film changes, so the coupling ratio of the propagation light changes accordingly, resulting in an intensity change in the output signal of the interferometer. The interferometer was applied for high-sensitive humidity sensing in the range of 20–80%, with a sensitivity of 0.21 dB/%RH and a fast rise time of 0.795 s. Thanks to its low cost, simple preparation method, and short manufacturing time, the humidity sensor proposed in this paper can be used in a wide range of applications in the fields of structural health testing, medical treatment, industrial production, and environmental monitoring.