Search Results (39)

This study aims to analyze the spatial and temporal distribution of traffic accidents between 2017 and 2021 and their underlying causes. Antalya (Turkey) was selected as the study area due to its significant seasonal population fluctuations, which influence traffic patterns. Geographic Information Systems (GIS) were employed to investigate the spatial and temporal interactions of factors contributing to accidents, categorized as internal (e.g., driver age, driver errors) and external (e.g., road density, holiday periods, and the effects of the COVID-19 pandemic). Accidents were classified by type (e.g., fatal, injury related) to identify critical areas for intervention. The Kernel Density Estimation method was employed to detect accident hotspots, while driver characteristics, accident outcomes, and age distributions were systematically analyzed. The obtained results reveal that most accidents involved drivers aged 20–39 years, primarily due to negligence or failure to adjust speed to road conditions. Seasonal variations and holiday periods were also found to influence the spatial distribution of accidents. A detailed evaluation of high-risk roundabouts using Torus software 6.1 identified a potential design deficiency at one specific roundabout. These results provide valuable insights for improving traffic safety and optimizing road infrastructure in regions experiencing dynamic population changes. Full article

The occurrence of knots as solutions of dynamical systems has been widely studied in the literature. In particular, ways to determine families of knots as solutions of differential equations have been described in several papers. In this article, an infinite family of dynamical systems, based on torus knots, is built each of which has the property that an infinite number of cable knots from torus knots (i.e., iterated torus knots) are obtained as solutions. One such dynamical system, based on the trefoil knot, is explicitly constructed. The methodology described herein may also be applied to any torus knot, and even to any other knot as long as a parametrization is provided for the latter. An example of application of the method is presented for the case of the figure eight knot, which is not a torus knot. Also, a possible application in cryptography is sketched. Full article

Objectives: Torus mandibularis (TM) is a benign bony exostosis on the lingual surface of the mandible, typically developing from the third decade of life with slow progression; its etiology remains unclear. As TM excision causes no functional or aesthetic disadvantages, its use as autologous bone graft material (e.g., for pre-implant or sinus lift augmentation) has been suggested. In this study, we investigate the prevalence and expression of TM in a southern German population with regard to age and gender. Additionally, we examine whether TM undergoes dynamic changes over time, with the hypothesis that TM may show temporal growth. Material and Methods: A retrospective analysis of CBCT scans from 210 randomly selected patients (105 males, 105 females) was performed. Patients were divided into three age groups (≤40, 41–60, ≥61 years; 70 per group), and TM was measured using OsiriX MD. For the longitudinal study, 146 CBCTs from 73 patients were compared over intervals of 2–9 years. Surface changes were assessed via 3D overlay using GOM Inspect. Results: TM was found in 30.5% of patients, and its prevalence was significantly higher in males (38%) than females (23%), with no age-related differences identified. Most TMs measured <2 mm (n = 51); only five exceeded this size. No dynamic growth was observed over time. Conclusion and Clinical Implications: TM is a common anatomical variant, more frequently detected through 3D imaging than clinical examination. In most cases, size remains minimal (<2 mm), limiting its clinical use as augmentation material in rare individual cases. Full article

A natural phenomenon in applications is the interaction of quasi-periodic solutions of dynamical systems in a dissipative setting. We study the interactions of two of such ODE systems based on the construction of a nonlinear oscillator with thermostatic (energy) control. This leads to the emergence of complexity, torus doubling, and chaos. We find canards; 1-, 2-, and 3-tori; chaos, and hyperchaos. Detailed analysis is possible in the case of small oscillations and small interactions. Large-scale phenomena are studied by the construction of charts of parameter space using Lyapunov exponents. Full article

To reduce the cost of offshore wind and wave power, an innovative combined wind–wave energy generation system constituting of a 15 MW semi-submersible floating offshore wind turbine (FOWT) and four torus-type wave energy converters (WECs) is proposed. A wholly coupled numerical model of aero-hydro-elastic-servo-mooring was built to evaluate the mooring line and motion dynamics of this novel combined system. Additionally, a practical mooring optimization framework is proposed with the Latin Hypercube sampling method, Kriging model, and the combined optimization techniques of the Genetic Algorithm and Gradient Algorithm. The optimization results demonstrate that the optimized mooring scheme satisfies all the strict constraints, validating the effectiveness of the optimization method. Moreover, the hydrodynamic characteristics of the combined system and the effects of the WECs on the mooring system under both rated and extreme conditions are discussed, including changes in time-series mooring tension, power spectral density, and statistical characteristics. The research findings provide a reference for the further development and optimization of this novel combined system, contributing to the efficient utilization of offshore renewable energy. Full article

The Dps protein is the major DNA-binding protein of prokaryotes, which protects DNA during starvation by forming a crystalline complex. The structure of such an intracellular DNA-Dps complex is still unknown. However, the phenomenon of a decrease in the size of the Dps protein from 90 Å to 69–75 Å during the formation of a complex with DNA has been repeatedly observed, and no explanation has been given. In this work, we show that during the formation of intracellular DNA–Dps crystals, the protein transitions to another oligomeric form: from a dodecameric (of 12 monomers), which has an almost spherical shape with a diameter of 90 Å, to a trimeric (of three monomers), which has a shape close to a torus-like structure with a diameter of 70 Å and a height of 40 Å. The trimer model was obtained through the molecular dynamic modeling of the interaction of the three monomers of the Dps protein. Placement of the obtained trimer in the electron density of in vitro DNA–Dps crystal allowed for the determination of the lattice parameters of the studied crystal. This crystal model was in good agreement with the SAXS data obtained from intracellular crystals of 2-day-old Escherichia coli cells. The final crystal structure contains a DNA molecule in the through channel of the crystal structure between the Dps trimers. It was discussed that the mechanism of protein transition from one oligomeric form to another in the cell cytoplasm could be regulated by intracellular metabolites and is a simple and flexible mechanism of prokaryotic cell transition from one metabolic state to another. Full article

This work proposes a new two-dimensional dynamical system with complete nonlinearity. This system inherits its nonlinearity from trigonometric and hyperbolic functions like sine, cosine, and hyperbolic sine functions. This system gives birth to infinite but countable coexisting attractors before and after being forced. These two megastable systems differ in the coexisting attractors’ type. Only limit cycles are possible in the autonomous version, but torus and chaotic attractors can emerge after transforming to the nonautonomous version. Because of the position of equilibrium points in different attractors’ attraction basins, this system can simultaneously exhibit self-excited and hidden coexisting attractors. This system’s dynamic behaviors are studied using state space, bifurcation diagram, Lyapunov exponents (LEs) spectrum, and attraction basins. Finally, the forcing term’s amplitude and frequency are unknown parameters that need to be found. The sparrow search algorithm (SSA) is used to estimate these parameters, and the cost function is designed based on the proposed system’s return map. The simulation results show this algorithm’s effectiveness in identifying and estimating parameters of the novel megastable chaotic system. Full article

This work investigates the enhancement of optical energy in the synchronized dynamics of three erbium-doped fiber lasers (EDFLs) that are diffusively coupled in a unidirectional ring configuration without the need for external pump modulation. Before the system shows stable high-energy pulses, different dynamic behaviors can be observed in the dynamics of the coupled lasers. The evolution of the studied system was analyzed using different techniques for different values of coupling strength. The system shows the well-known dynamic behavior towards chaos at weak coupling, starting with a fixed point at low coupling and passing through Hopf and torus bifurcations as the coupling strength increases. An interesting finding emerged at high coupling strengths, where phase locking occurs between the frequencies of the three lasers of the system. This phase-locking leads to a significant increase in the peak energy of the EDFL pulses, effectively converting the emission into short, high amplitude pulses. With this method, it is possible to significantly increase the peak energy of the laser compared to a continuous EDFL single pulse. Full article

Preplanetary nebulae (PPNe) are formed from mass-ejecting late-stage AGB stars. Much of the light from the star gets scattered or absorbed by dust particles, giving rise to the observed reflection nebula seen at visible and near-IR wavelengths. Precursors to planetary nebulae (PNe), PPNe generally have not yet undergone any ionization by UV radiation from the still-buried stellar core. Bipolar PPNe are a common form of observed PPNe. This study lays the groundwork for future dynamical studies by reconstructing the dust density distribution of a particularly symmetric bipolar PPN, M1-92 (Minkowski’s Footprint, IRAS 19343+2926). For this purpose, we develop an efficient single-scattering radiative transfer model with corrections for double-scattering. Using a V-band image from the Hubble Space Telescope (HST), we infer the dust density profile and orientation of M1-92. These results indicate that M1-92’s slowly expanding equatorial torus exhibits an outer radial cutoff in its density, which implicates the influence of a binary companion during the formation of the nebula. Full article

Finite-dimensional equations constructed earlier to describe the motion of an aquatic drop-shaped robot due to given rotor oscillations are studied. To study the equations of motion, we use the Poincaré map method, estimates of the Lyapunov exponents, and the parameter continuation method to explore the evolution of asymptotically stable solutions. It is shown that, in addition to the so-called main periodic solution of the equations of motion for which the robot moves in a circle in a natural way, an additional asymptotically stable periodic solution can arise under the influence of highly asymmetric impulsive control. This solution corresponds to the robot’s sideways motion near the circle. It is shown that this additional periodic solution can lose stability according to the Neimark–Sacker scenario, and an attracting torus appears in its vicinity. Thus, a quasiperiodic mode of motion can exist in the phase space of the system. It is shown that quasiperiodic solutions of the equations of motion also correspond to the quasiperiodic motion of the robot in a bounded region along a trajectory of a rather complex shape. Also, strange attractors were found that correspond to the drifting motion of the robot. These modes of motion were found for the first time in the dynamics of the drop-shaped robot. Full article

We numerically investigate the dynamics of a ring consisting of three unidirectionally coupled Erbium-Doped Fiber Lasers (EDLFs) without external pump modulation. The study focuses on the system behavior as the coupling strength is varied, employing a six-dimensional mathematical model that includes three variables for laser intensities and three variables for population inversions of all lasers. Our primary objective is to understand the system evolution towards chaos from a stable equilibrium in the ring, considering the impact of increasing coupling strength. To analyze the system’s behavior, we employ various techniques such as time series analysis, power spectra, Poincaré sections, bifurcation diagrams, and Lyapunov exponents. During the transition to chaos, the system undergoes a Hopf bifurcation and a series of torus bifurcations. An essential aspect of this study is the exploration of a rotating wave propagating along the ring, where the wave nature (periodic, quasiperiodic, or chaotic) depends on the coupling strength. Additionally, we observe the coexistence of periodic and chaotic orbits within a specific range of the coupling strength. However, for very strong coupling, this bistability disappears, resulting in a monostable system with a single limit cycle. This regime exhibits potential for applications that demand short laser pulses with a substantial increase in peak power, reaching nearly 20 times higher levels compared to the continuous mode when the lasers are uncoupled. This discovery holds particular importance for optical communication systems, especially considering the attenuation optical signals experience when transmitted over long distances. Full article

Canards are a type of transient dynamics that occur in singularly perturbed systems, and they are specific types of solutions with varied dynamic behaviours at the boundary region. This paper introduces the emergence and development of canard phenomena in a neuron model. The singular perturbation system of a general neuron model is investigated, and the link between the transient transition from a neuron model to a canard is summarised. First, the relationship between the folded saddle-type canard and the parabolic burster, as well as the firing-threshold manifold, is established. Moreover, the association between the mixed-mode oscillation and the folded node type is unique. Furthermore, the connection between the mixed-mode oscillation and the limit-cycle canard (singular Hopf bifurcation) is stated. In addition, the link between the torus canard and the transition from tonic spiking to bursting is illustrated. Finally, the specific manifestations of these canard phenomena in the neuron model are demonstrated, such as the singular Hopf bifurcation, the folded-node canard, the torus canard, and the “blue sky catastrophe”. The summary and outlook of this paper point to the realistic possibility of canards, which have not yet been discovered in the neuron model. Full article

In the past few years, the Event Horizon Telescope (EHT) has provided the first-ever event horizon-scale images of the supermassive black holes (BHs) M87${}^{*}$ and Sagittarius A${}^{*}$ (Sgr A${}^{*}$). The next-generation EHT project is an extension of the EHT array that promises larger angular resolution and higher sensitivity to the dim, extended flux around the central ring-like structure, possibly connecting the accretion flow and the jet. The ngEHT Analysis Challenges aim to understand the science extractability from synthetic images and movies to inform the ngEHT array design and analysis algorithm development. In this work, we compare the accretion flow structure and dynamics in numerical fluid simulations that specifically target M87${}^{*}$ and Sgr A${}^{*}$, and were used to construct the source models in the challenge set. We consider (1) a steady-state axisymmetric radiatively inefficient accretion flow model with a time-dependent shearing hotspot, (2) two time-dependent single fluid general relativistic magnetohydrodynamic (GRMHD) simulations from the H-AMR code, (3) a two-temperature GRMHD simulation from the BHAC code, and (4) a two-temperature radiative GRMHD simulation from the KORAL code. We find that the different models exhibit remarkably similar temporal and spatial properties, except for the electron temperature, since radiative losses substantially cool down electrons near the BH and the jet sheath, signaling the importance of radiative cooling even for slowly accreting BHs such as M87${}^{*}$. We restrict ourselves to standard torus accretion flows, and leave larger explorations of alternate accretion models to future work. Full article

Establishing the aeroelastic characteristic of all-movable fins with freeplay nonlinearities is one of the most common problems in the design of supersonic flight vehicles. In this context, this study provided novel points of view on the nonlinear aeroelastic characteristics of an all-movable fin with freeplay nonlinearities in its root. The unsteady aerodynamic model that was employed uses the second-order piston theory considering thickness effects. For a system with multiple freeplay nonlinearities, a discrete scanning method based on the describing function method was established to solve the limit-cycle oscillations (LCOs) and avoid the loss of solutions. Combining this with the time-domain integration method, the influences of the support stiffness at the root of the fin and the freeplay size ratio of the bending and torsional degrees of freedom on the dynamical response of the system were analyzed. The results demonstrate that systems with a single freeplay nonlinearity exhibit two completely different types of LCO, while systems with multiple freeplay nonlinearities exhibit complex dynamical behaviors such as LCO and quasi-periodic and chaotic motions. The path of a quasi-periodic torus breaking into chaos was observed. Furthermore, a harmonic initial condition for the time-domain integration is proposed; this can be used for a quick check of the frequency-domain calculation results. Full article

To increase the utilization of wave and other renewable energy resources, an integrated system consisting of an offshore wind turbine and a wave energy converter (WEC) could be used to harvest the potential energy. In this study, a dimensionless optimization method is developed for shape optimization of a hollow cylindrical WEC, and an optimal shape is obtained using a differential evolution (DE) algorithm. The frequency domain response characteristics of the WEC with different geometric shapes and viscous damping loads are studied. The numerical model of the wind-wave integrated system, which consists of a semisubmersible platform and the WEC, is developed and used. The dynamic responses of the integrated system with and without using the WEC optimum section are compared. The results show that the dimensionless optimization method utilized in this paper is very applicable for hollow cylindrical WECs. A smaller inner radius and larger draft increase the heave RAO amplitude of the WEC significantly. In addition, optimization of the WEC shape and power take-off (PTO) damping coefficient can significantly improve the energy capture of the integrated system, which increases by 32.03%. The research results of this paper provide guidance for achieving the optimum design of offshore wind-wave energy integrated systems and quantify the benefits of using optimum designs in the produced wave energy power. In addition, the proposed dimensionless optimization method is generic and can be widely applied to different types of WECs. Full article