Close Trajectories Research Articles

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations.

Large stochastic population abundance fluctuations are ubiquitous across the tree of life, impacting the predictability and outcomes of population dynamics. It is generally thought that abundance fluctuations with a Taylor's law exponent of two do not strongly impact evolution. However, we argue that such abundance fluctuations can lead to substantial genotype frequency fluctuations if different genotypes in a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related Escherichia coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from genetic drift. We develop an effective model explaining that the abundance fluctuations arise from correlated offspring numbers between individuals, and the large frequency fluctuations result from (even slight) decoupling in offspring number correlations between genotypes. The model quantitatively predicts the observed abundance and frequency fluctuation scaling. Initially close trajectories diverge exponentially, suggesting that chaotic dynamics may underpin the excess frequency fluctuations. Our findings suggest that decoupling noise is also present in mixed-genotype Saccharomyces cerevisiae populations. Theoretical analyses demonstrate that decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of these frequency fluctuations, we expect them to be widespread across biological populations.

A UNIVERSAL ALGORITHM FOR ESTIMATING THE LYAPUNOV EXPONENT IN A DISSIPATIVE DYNAMICAL SYSTEM

When studying dynamic systems, it often becomes necessary to quantify the degree of chaotization of the dynamic regime. The presence of a positive Lyapunov exponent in the system indicates a rapid divergence over time of any two close trajectories and sensitivity to the values ​​of the initial conditions. At the same time, the chaotic attractor geometry can be complex, contain both divergent and convergent trajectories. For such attractors, the Bennettin algorithm will give an underestimated small value. This is due to the fact that the section of convergence of the trajectories is included in the average value with a minus sign. But by definition, a strange attractor, like any attractor of a dissipative dynamical system, is limited in phase space, so the distance between the representing points on it will necessarily be either large or small. A modification of the Bennettin algorithm is proposed, which makes it possible to take into account both the divergence and the convergance of the trajectory on the attractor of a dissipative dynamical system. The method is applied to a strange attractor in the cross-waves hydrodynamic system. Estimation of the Lyapunov exponent based on the classical Benettin algorithm does not take into account the convergence and divergence of trajectories on a chaotic attractor. The article proposes a universal algorithm, the accuracy of which does not depend on this and other features of chaotic attractors, such as their shape, size, and structure, as well as their number and location in phase space. The new algorithm makes it possible to increase the accuracy of calculations and expand the field of application of the method. The application of the proposed modification to the model of excitation of cross-shaped waves on the free surface of a liquid in a rectangular channel of finite length and depth made it possible to more accurately identify the dynamic regime.

Observing quantum matter-wave diffraction in the energetic He2+-He collisions

We present an experiment combined with numerical simulations to study single and double electron capture processes induced during the collisions between the He target and the He2+ projectile in the energy range 2–20 keV/u. According to our experimental observations, measuring the angular distribution of the scattered projectile He2+ reveals a clear oscillatory structure. The latter records an imprint of the collision dynamics, specifically, a signature of the matter-wave scattering and the internal electronic structure of the collisional system He2+-He. We found that this feature is sensitive to the incident projectile's energy and the nature of the involved process. With the help of four-body semiclassical close coupling and classical trajectory Monte Carlo methods, we show that the observed structure is of a quantum nature. This is further supported by a simple mathematical model based on Fraunhofer-type diffraction of light, to which the oscillations are attributed. Our findings thus provide insights into the role of quantum phenomena in characterizing collision dynamics. Published by the American Physical Society 2024

RL-Based Detection, Tracking, and Classification of Malicious UAV Swarms through Airborne Cognitive Multibeam Multifunction Phased Array Radar

Detecting, tracking, and classifying unmanned aerial vehicles (UAVs) in a swarm presents significant challenges due to their small and diverse radar cross-sections, multiple flight altitudes, velocities, and close trajectories. To overcome these challenges, adjustments of the radar parameters and/or position of the radar (for airborne platforms) are often required during runtime. The runtime adjustments help to overcome the anomalies in the detection, tracking, and classification of UAVs. The runtime adjustments are performed either manually or through fixed algorithms, each of which can have its limitations for complex and dynamic scenarios. In this work, we propose the use of multi-agent reinforcement learning (RL) to carry out the runtime adjustment of the radar parameters and position of the radar platform. The radar used in our work is a multibeam multifunction phased array radar (MMPAR) placed onboard UAVs. The simulations show that the cognitive adjustment of the MMPAR parameters and position of the airborne platform using RL helps to overcome anomalies in the detection, tracking, and classification of UAVs in a swarm. A comparison with other artificial intelligence (AI) algorithms shows that RL performs better due to the runtime learning of the environment through rewards.

Analisis Kebutuhan Frekuensi Kapal Ro-Ro Dalam Melayani Penyeberangan

Air Putih - Sei Selari crossing of Bengkalis regency has a distance of 5 miles. The total number of Ro-Ro vessels operating at the parallel crossing of Air Putih – Sei Selari is 6 vessels with a rolling system where 4 vessels operate and 2 vessels are off / standby. The number of trips served per day is an average of 20 trips. However, the overall number of ships operating on a fairly close trajectory is not balanced with optimal ship operating time service. As a result there is a queue of ships to dock. In this study used several methods of analysis to solve the problems that occur, including load factor analysis, frequency analysis required and analysis of the needs of the number of ships. From the results of the analysis it was found that the ideal number of ship frequencies under normal and congested conditions were 21 trips/day and 24 trips/day respectively. Scheduling is based on ship service time during normal and busy times, both of that condition have Sailing Time 35 minutes, headways 90 minutes at normal condition and 103 minutes at congested, Layover time 20 minutes at normal times and 25 minutes at congested, so as to minimize the length of waiting time for ships to dock on the wharf. With a total of 6 ships, the ship operating schedule per day uses a ship rolling system with the division of 3 ships in operation and 3 ships off / standby.

Formation Flying Lyapunov-Based Control Using Lorentz Forces

A formation flying control algorithm using the Lorentz force for Low Earth Orbits to achieve a trajectory with required shape and size is proposed in the paper. The Lorentz force is produced as a result of interaction between the Earth’s magnetic field and an electrically charged spacecraft. Achievement of the required trajectories represents a challenge since the control in three-dimensional space is a scalar value of the satellite’s charge. A Lyapunov-based control algorithm is developed for elimination of the initial relative drift after the launch. It also aims at reaching a required amplitudes for close relative trajectories for in-plane and out-of-plane motion. Due to the absence of full controllability, the algorithm is incapable of correcting all the parameters of the relative trajectory such as in-plane and out-of-plane phase angles. The proposed control allows to converge to the trajectory with required shape and size, though with some oscillating errors in the vicinity of the required trajectory parameters. Numerical simulation of the relative motion is used to study performance of the control algorithm for one case of one controlled satellite and two cases of five controlled satellites forming a nested ellipses and train formations. The convergence time and final trajectory accuracy are evaluated for different control parameters and orbits using Monte Carlo approach.

Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms

Most of the existing methods and techniques for the detection of chaotic behaviour from empirical time series try to quantify the well-known sensitivity to initial conditions through the estimation of the so-called Lyapunov exponents corresponding to the data generating system, even if this system is unknown. Some of these methods are designed to operate in noise-free environments, such as those methods that directly quantify the separation rate of two initially close trajectories. As an alternative, this paper provides two nonlinear indirect regression methods for estimating the Lyapunov exponents on a noisy environment. We extend the global Jacobian method, by using local polynomial kernel regressions and local neural net kernel models. We apply such methods to several noise-contaminated time series coming from different data generating processes. The results show that in general, the Jacobian indirect methods provide better results than the traditional direct methods for both clean and noisy time series. Moreover, the local Jacobian indirect methods provide more robust and accurate fit than the global ones, with the methods using local networks obtaining more accurate results than those using local polynomials.

Chen system-based chaotic transceiver for frequency output quartz transducers

The application of unidirectional synchronization of two coupled Chen systems is exhibited in this work. In spite of the high dependence on initial conditions, which means that two initially close phase trajectories with time become uncorrelated, it is possible to synchronize two dynamic systems to make them evolve identically. Data transmission using chaos requires mixing an information signal with a chaotic carrier. This procedure performs data encryption and spreads the spectrum of an information signal, which increases information security and reliability. Thus, the prospect of using devices with chaotic dynamics in modern telecommunication and telemetry applications is due to several factors, including high information capacity, various frequencies, and confidentiality of messages. The proposed scheme is considered to be used in a measuring transducer design that requires sensors to operate at a long distance from the rest of the scheme. We propose an application of a chaotic oscillator as a transceiver module for a quarts sensor transducer, which could be used in a telemetry application. The process of producing non-periodic but determined oscillations by the non-linear Chen system and signal transmission application, based on it, are the subject of the research. The complete synchronization of two unidirectionally connected Chen systems and its signal transmission application are considered. The goal is to develop a transceiver extension for the quartz measuring transducer scheme to ensure the stable operation of sensors at a long distance from the rest of the scheme. The result of the research: a chaos synchronization scheme was applied to transmit a frequency-modulated signal, obtained from a difference-frequency block of the quartz sensor transducer. Additionally, the mathematical model and numerical modeling of the Chen dynamical system has been done. The numerical solution of the system's differential equations was obtained using Matlab software. To study the change in the dynamic regime depending on the parameters of the model, the spectrum of Lyapunov exponents was calculated and bifurcation diagrams were constructed. The circuit design of the Chen oscillator was built using Multisim software, which uses the PSpice model to simulate electrical components. A model of an analog signal transmission system with chaotic mixing of a frequency output signal with a chaotic carrier has been proposed as an extension of the use of quartz transducers in measuring devices.

Detecting chaos in lineage-trees: A deep learning approach

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in understanding these processes. Classifying a system as chaotic entails estimating its largest Lyapunov exponent (LLE), which quantifies the average rate of convergence or divergence of initially close trajectories in state space. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in low-dimensional systems affected by a small amount of dynamical noise, which are used to model many real-world processes, and in particular biological systems. We describe a method for accurately estimating the largest Lyapunov exponent from noisy data, based on training deep learning models on synthetically generated trajectories. Once the deep learning models are trained, they can be used to detect the LLE from empirical data without any assumption on the underlying dynamics. Our method naturally extends to different input topologies, allowing us to analyze tree-shaped data, characteristic of inheritance dynamics, where near-identical replication offers a unique and hitherto unstudied avenue to detect chaos. We also characterize the input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.

Collisions of antiprotons with excited positronium atoms

A detailed theoretical investigation of the fundamental three-body antiproton-positronium system is presented, utilizing both quantum convergent close coupling and classical trajectory methods. We evaluate scattering cross sections for all major processes, including charge transfer and breakup, over a wide range of positronium kinetic energies and states with principal quantum number ${n}_{\mathrm{Ps}}\ensuremath{\le}6$. The study has significantly extended previous work, and the direct quantum-classical comparison has revealed a systematic approach to obtaining cross sections for arbitrarily high ${n}_{\mathrm{Ps}}$. This is of major significance for prospective applications of collisions of excited positronium atoms in cold (anti-)atomic physics.

On the limit cycles for a class of generalized Liénard differential systems

The main aim of the present paper is to study the existence of limit cycles (i.e. close trajectories in the phase space having the property that at least one other trajectory spirals into them either as time approaches infinity or as time approaches negative infinity) of a class of piecewise generalized Liénard differential system modulated by a two variable polynomial and a piecewise linear function respectively. The main tool that we use to obtain these results is the averaging theory of the dynamical systems worthy to detect the initial conditions of the birth of isolated orbits of a system.

Multi-UAV Trajectory Optimization Considering Collisions in FSO Communication Networks

In this paper, a trajectory optimization algorithm for multiple unmanned aerial vehicles (UAVs) is investigated for free space optic (FSO) based wireless communication networks, which is composed of multiple UAVs and multiple ground terminals (GTs). Considering the FSO channel model and line of sight (LoS) probability, the altitude of the UAVs for FSO connection between each GT and UAV is decided by the predetermined radius of the communication area of the GT. A multi-UAV trajectory optimization (MUTO) scheme is proposed to maximize the service time. In the MUTO scheme, first, the network is divided into multiple sectors using graph partitioning, and assigned to each UAV, and then the traveling salesman problem (TSP) is used to determine the order of the GTs that the UAV passes through. The number of UAVs that maximizes the time for the UAV to stay within the communication area of the GT is derived. The UAV trajectories are determined by sequentially minimizing the energy consumed when moving between GTs and maximizing the service time by applying successive convex approximation. In addition, to assist operations that use multiple UAVs, two collision avoidance schemes are applied to the MUTO scheme. First is the additional constraints (AC) method, which uses a geographic formula to control the distance between the UAVs, and second is the initial delay (ID) method, which deliberately adds a delay to the UAV trajectories to provide sufficient UAV spacing. The simulation results show that under low density operation conditions, MUTO-ID and MUTO-AC are sufficient to avoid all UAV collisions, and in overly dense UAV operations with very close UAV trajectories, MUTO-ID can reduce collisions by approximately 80%, MUTO-AC can reduce collisions by approximately 85%, and MUTO-ACID can reduce collisions by approximately 95%, when compared to the MUTO scheme with no collision avoidance support applied.

Toward immersive spacecraft trajectory design: Mapping user drawings to natural periodic orbits

This paper presents an immersive spacecraft trajectory design application within the cislunar space domain. The long-term goal of this application is to enable users to design spacecraft trajectories by drawing curves while immersed in a three-dimensional (3D) virtual reality replica of the Earth–Moon system. In this framework, visual memory or understanding of orbit dynamics may be directly linked to the creation of trajectory baselines for preliminary mission design with 3D drawings. An orthogonal-collocation-based optimizer maps user-drawn curves to approximate orbit solutions that are feasible under the natural dynamics of the Earth–Moon system. The natural dynamics of the Earth–Moon system are modeled using a circular-restricted three-body problem (CR3BP) model. Two experiments are conducted to initially assess the feasibility of the proposed trajectory design framework and to determine the robustness of the optimizer in the presence of user-induced distortions within the 3D user drawings. The first experiment establishes that it may be feasible to map a user-drawn curve to a close natural CR3BP trajectory. In fact, during the experiment, sample user-drawn curves were mapped to natural CR3BP orbits with a seventy-five percent success rate. The second experiment establishes baseline statistics for user-induced distortions over one hundred and three user-drawn traces of a sample L2 halo reference orbit. Based on these statistics, a final analysis provides a quantitative measure in verification of the robustness of the optimizer when user-induced distortions are present. Hence the proposed immersive computing framework is deemed suitable for further development for trajectory design in cislunar space.

Spin stability of a binary black hole coalescence

We analyze the spin stability of a binary black hole coalescence when the binary system is described by the Post-Newtonian (PN) equations in the adiabatic regime. The main idea in this work is to make a massive exploration of the solution space in search of chaos. For that, we evolve the PN equations using a CUDA implementation of the RKF78 scheme and study the dynamical behavior of the system. Each initial spin configuration run in the GPU is composed by more than 80000 simulations. The chaos indicator used to characterize the degree of separation of two infinitesimally close trajectories is the Lyapunov exponent. We find zones in the solution space where the separation between nearby trajectories reaches several orders of magnitude bigger than the initial separation. Also, we note that the chaotic behavior can be observed in forward as well as in backward evolution.

Quartic polynomial approximation for fluctuations of separation of trajectories in chaos and correlation dimension

We consider the cumulant generating function of the logarithm of the distance between two infinitesimally close trajectories of a chaotic system. Its long-time behavior is given by the generalized Lyapunov exponent providing the logarithmic growth rate of the kth moment of the distance. The Legendre transform of is a large deviations function that gives the probability of rare fluctuations where the logarithmic rate of change of the distance is much larger or much smaller than the mean rate defining the first Lyapunov exponent. The only non-trivial zero of is at minus the correlation dimension of the attractor which for incompressible flows reduces to the space dimension. We describe here general properties constraining the form of and the Gallavotti–Cohen type relations that hold when there is symmetry under time-reversal. This demands studying joint growth rates of infinitesimal distances and volumes. We demonstrate that quartic polynomial approximation for does not violate the Marcinkiewicz theorem on invalidity of polynomial form for the generating function. We propose that this quartic approximation will fit many experimental situations, not having the effective time-reversibility and the short correlation time properties of the quadratic Grassberger–Procaccia estimates. We take the existing for turbulent channel flow and demonstrate that the quartic fit is nearly perfect. The violation of time-reversibility for the Lagrangian trajectories of the incompressible Navier–Stokes (NS) turbulence below the viscous scale is considered. We demonstrate how the fit can be used for finding the correlation dimensions of strange attractors via easily measurable quantities. We provide a simple formula via the Lyapunov exponents, holding in quadratic approximation, and describe the construction of the quartic approximation. A different approximation scheme for finding the correlation dimension from expansion in the flow compressibility is also provided.

Quantum Limitation to the Coherent Emission of Accelerated Charges.

Accelerated charges emit electromagnetic radiation. According to classical electrodynamics, if the charges move along sufficiently close trajectories they emit coherently; i.e., their emitted energy scales quadratically with their number rather than linearly. By investigating the emission by a two-electron wave packet in the presence of an electromagnetic plane wave within strong-field QED, we show that quantum effects deteriorate the coherence predicted by classical electrodynamics even if the typical quantum nonlinearity parameter of the system is much smaller than unity. We explain this result by observing that coherence effects are also controlled by a new quantum parameter which relates the recoil undergone by the electron to the width of its wave packet in momentum space.

Acceleration of Plasma in Coaxial Channels with Preshaped Electrodes and Longitudinal Magnetic Field

The paper presents a mathematical model and results of numerical simulation of axisymmetric plasma flows in nozzle-type channels formed by two coaxial electrodes. Transonic accelerated flows, which are of interest for the development of plasma accelerators, are considered. The mathematical apparatus of the models are two-dimensional MHD problems solved numerically, the steady-state solutions of which are obtained in the process of relaxation. Some characteristics of the flow in narrow tubes between close trajectories are considered in the quasi-one-dimensional approximation. The main attention is paid to the influence of the longitudinal magnetic field and the curvilinear geometry of the electrodes on the properties of accelerated flows.

Observation of Stable Sound Field Components in Lake Ladoga

The paper presents the results of processing measurement data on the spatiotemporal structures of sound fields in Lake Ladoga. Measurements were taken with an extended vertical receiver array. The aim of processing was to isolate the field components that were stable with respect to small variations in the waveguide parameters. Since a model of the medium is inevitably inaccurate, such components can be predicted with greater accuracy than the total field. In terms of the ray approach, a stable component is generated by a beam of rays propagating over close trajectories. The discussed experiment analyzed sound fields excited by a point source that emitted wideband pulses, as well as the fields of wave beams excited by the emitting vertical array at fixed frequencies. In both cases, the processing results showed that the isolated stable components, as expected, coincide substantially better with the prediction of theoretical calculation (by the wide angle parabolic equation method) than with the total wave field.

On the optimal passive formation reconfiguration by using attitude control

The possibility to reconfigure satellite formations with utilization of the drag and the solar radiation pressure has been established with previous works. Passive formation reconfiguration maneuvers may be achieved by controlling the attitude of the satellites and varying the area exposed to the perturbation forces. This paper deals with the development of a simple but effective model to understand the possibilities offered by this kind of maneuvers. Limits and advantages of the presented maneuvers are examined considering different reconfigurations maneuvers among close relative trajectories in Low Earth Orbits, Medium Earth Orbits and Geostationary Orbits. The theoretical investigations are confirmed by numerical simulations where the Inverse Dynamics Particle Swarm Optimization is employed. The relative dynamics is simulated with a high-fidelity orbital simulator considering all the perturbations affecting the spacecrafts orbits and the gravity gradient torque influencing the attitude dynamics. Several test cases are reported to underline all the possibilities offered by the proposed maneuvering strategy.

Chaotic Properties of a Turbulent Isotropic Fluid.

By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent λ and the Reynolds number Re is measured using direct numerical simulations, performed on up to 2048^{3} collocation points. The Lyapunov exponent is found to solely depend on the Reynolds number with λ∝Re^{0.53} and that after a transient period the divergence of trajectories grows at the same rate at all scales. Finally a linear divergence is seen that is dependent on the energy forcing rate. Links are made with other chaotic systems.