Classical Dynamics Research Articles

A generalized Bogdanov-Takens system with arbitrary degree

The aim of this paper is to give the bifurcation diagram and all global phase portraits in the Poincaré disc of a generalized Bogdanov-Takens system with arbitrary degree. Moreover, the system has abundant nonlinear phenomena, such as double limit cycle bifurcation, Hopf bifurcation, homoclinic bifurcation, heteroclinic bifurcation, and so on. Notice that the nonlinear phenomena of the system are more abundant and more complex than the classic Bogdanov-Takens system.

On the role of geometric phase in the dynamics of elastic waveguides.

The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Controller design and remote piloting training module development for unmanned cropped delta reflex wing configuration

In this study, a cost-effective high-fidelity six-degree of freedom module augmented with an onboard controller is developed. The unmanned aerial vehicle (UAV) under consideration is a wing-alone configuration with a cropped delta planform and reflex airfoil cross-section designed to perform manoeuvres at high angles of attack. The six-degree of freedom dynamics for the aforementioned configuration is developed based on Newtonian mechanics incorporating linear and nonlinear aerodynamic models to expand flight simulations in corresponding regimes. Aerodynamic stability and control parameters for the simulations are obtained from full-scale wind tunnel measurements and flight tests. It is observed that the linear aerodynamic model is valid in angle of attack (α) domain −5°≤α≤10°, followed by nonlinearity up to α≈21°, post which lift coefficient remains almost constant with angle of attack till 45°. The simulation model is validated with the corresponding flight data obtained from flight tests. A user-friendly graphical interface with real-time animation of UAV has been developed for the aforementioned configuration by integrating MATLAB and Flightgear environment with real-time control input from the hardware to enable the pilot for visual and tactile feedback, respectively. A controller based on total energy control is designed for velocity and altitude hold modes, while an attitude hold controller is designed for pitch and roll angle tracking to enable controller-in-the-loop remote piloting simulations. In order to enhance practical applicability, the designed module has been tested under various simulated wind conditions. It is noticed from the results that the steady-state error in attitude remains below 2% with a maximum overshoot of 5° from reference. The total energy controller achieves a zero steady-state error with a maximum overshoot of 2 m/s for velocity and 6 m for altitude, respectively. The developed module enhances remote piloting training, flight response assessment, and control algorithm testing for cropped delta planform UAVs.

Massive twistor worldline in electromagnetic fields

We study the (ambi-)twistor model for spinning particles interacting via electromagnetic field, as a toy model for studying classical dynamics of gravitating bodies including effects of both spins to all orders. We compute the momentum kick and spin kick up to one-loop order and show precisely how they are encoded in the classical eikonal. The all-orders-in-spin effects are encoded as a dynamical implementation of the Newman-Janis shift, and we find that the expansion in both spins can be resummed to simple expressions in special kinematic configurations, at least up to one-loop order. We confirm that the classical eikonal can be understood as the generator of canonical transformations that map the in-states of a scattering process to the out-states. We also remark that cut contributions for converting worldline propagators from time-symmetric to retarded amount to the iterated action of the leading eikonal at one-loop order.

A novel scale-bridging method for MSMA linking continuum thermodynamics constitutive formulations to lumped system-level models

This work introduces a novel scale-bridging method between a continuum thermodynamics constitutive model and a lumped system-level model for magnetic shape memory alloys (MSMA). With this method, system models for real-time operations are generated based on virtual experiments using the constitutive model. The proposed method addresses the fact that, while constitutive models for MSMA typically only require small sets of parameters as input, their evaluation is still computationally expensive. System models for control engineering, however, require extensive experimental parameterization, while their evaluation is highly time-efficient. The proposed scale-bridging method has the potential to combine a small parameterization effort and a low computational cost of the real-time system model. Additionally, the constitutive model is utilized to investigate whether it can determine the individual behavior of MSMA samples. This is important since the inherent model parameters, while valid for ideal single crystals, deviate for non-ideal MSMA sample behavior. To this end, the MSMA constitutive model, based on a global variational principle originally proposed by Kiefer et al is supplemented by various extensions, including a more robust algorithmic treatment. A parameter identification procedure is introduced to optimize the constitutive model parameters based on an outer hysteresis curve for a particular load case. By conducting virtual experiments with the constitutive model, data sets are generated to parameterize Preisach hysteresis models as numerical approximations of the constitutive models. The resulting hysteresis models are compared with physical experiments using an MSMA test bench for different load cases. It is shown that the proposed scale-bridging method successfully generates hysteresis models derived from constitutive models. While maintaining accuracy comparable to strictly phenomenological models across various load cases (as validated through physical MSMA test bench experiments), these models require significantly less parameterization effort than classical system models. This translates to faster model creation and broader applicability.

Corrections to Diffusion in Interacting Quantum Systems

The approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor ⟨n(x,t)n⟩, in the presence of a single U(1) or SU(2) charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1D Floquet systems with conserved magnetization. We find a qualitative agreement with EFT, which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore nonlinear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the nonlinear phenomena present in thermalizing systems. Published by the American Physical Society 2024

Observables from the spinning eikonal

We study the classical dynamics of spinning particles using scattering amplitudes and eikonal exponentiation. We show that observables are determined by a simple algorithm. A wealth of complexity arises in perturbation theory as positions, momenta and spins must be iteratively corrected at each order. Even though we restrict ourselves to one-loop computations at quadratic order in spin, nevertheless we encounter and resolve a number of subtle effects. Finally, we clarify the links between our work and various other eikonal approaches to spinning observables.

Unification, T-theoreticity, and Testing: The Case of Fitness in Natural Selection

AbstractTheoreticity and unification are two main issues discussed in philosophy of science. The first attempts to clarify the different roles of concepts used in a scientific theory. The second concerns the role of unification in scientific explanation and scientific progress. Both discussions have followed separate, independent paths. In this paper, we examine the interrelatedness of these two notions by focusing on classical particle mechanics and the theory of natural selection. We claim that they are interconnected in two distinct ways. On the one hand, a theory’s unifying power relies on the presence of some theoretical concepts that apply to heterogeneous phenomena through the assumption of a (sometimes unstated) general principle. On the other hand, a sensible application of the theoreticity criterion to these integrating concepts requires the unification not being spurious. We conclude that a correct determination of the theoreticty status requires analyzing how specific applications of different parts of a theory interact with each other.

Deep Learning Methods to Analyze the Forces and Torques in Joints Motion

This paper proposes a composite model that combines convolutional neural network models and mechanical analysis to determine the forces acting on an object. First, we establish a model using Newtonian mechanics to analyze the forces experienced by the human body during movement, particularly the forces on joints. The model calculates the mapping relationship between the object’s movement and the forces on the joints. Then, by analyzing a large number of fencing competition videos using a deep learning model, we extract video features to study the torques and forces on human joints. Our analysis of numerous images reveals that, in certain movement patterns, the peak pressure on the knee joint can be two to three times higher than in a normal state, while the driving knee can withstand peak torques of 400–600 Nm. This straightforward model can effectively capture the forces and torques on the human body during movement using a deep neural network. Furthermore, this model can also be applied to problems involving non-rigid body motion.

Zhukovsky-Volterra top and quantisation ideals

In this letter, we revisit the quantisation problem for a fundamental model of classical mechanics—the Zhukovsky-Volterra top. We have discovered a four-parametric pencil of compatible Poisson brackets, comprising two quadratic and two linear Poisson brackets. Using the quantisation ideal method, we have identified two distinct quantisations of the Zhukovsky-Volterra top. The first type corresponds to the universal enveloping algebras of so(3), leading to Lie-Poisson brackets in the classical limit. The second type can be regarded as a quantisation of the four-parametric inhomogeneous quadratic Poisson pencil. We discuss the relationships between the quantisations obtained in our paper, Sklyanin's quantisation of the Euler top, and Levin-Olshanetsky-Zotov's quantisation of the Zhukovsky-Volterra top.

Intensity-Product-Based Optical Sensing to Beat the Diffraction Limit in an Interferometer.

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.

CRISPR-Cas13d as a molecular tool to achieve targeted gene expression knockdown in chick embryos.

The chick embryo is a classical model system commonly used in developmental biology due to its amenability to gene perturbation experiments. Pairing this powerful model organism with cutting-edge technology can significantly expand the range of experiments that can be performed. Recently, the CRISPR-Cas13d system has been successfully adapted for use in zebrafish, medaka, killifish, and mouse embryos to achieve targeted gene expression knockdown. Despite its success in other animal models, no prior study has explored the potential of CRISPR-Cas13d in the chick. Here, we present an adaptation of the CRISPR-Cas13d system to achieve targeted gene expression knockdown in the chick embryo. As proof-of-principle, we demonstrate the knockdown of PAX7, an early neural crest marker. Application of this adapted CRISPR-Cas13d technique resulted in effective knockdown of PAX7 expression and function, comparable to knockdown achieved by translation-blocking morpholino. CRISPR-Cas13d complements preexisting knockdown tools such as CRISPR-Cas9 and morpholinos, thereby expanding the experimental potential and versatility of the chick model system.

Precipitation of the gamma prime phase in a Ni-co-based superalloy during different stages of cooling

The cooling precipitation of the gamma primary (γ') phase in a precipitation strengthened Ni-Co-base disk superalloy was investigated by various experimental and analytical methods. The alloy was super-solvus heat treated and then slow cooled to different interrupted temperatures (IT) followed by instant water quenching. It shows that with the IT change, the γ' phase precipitated in different characteristics, such as morphologies, sizes and distributions. Through using three-dimensional atomic probe (3DAP) technique to study the γ and γ' compositions and their interface composition profiles, three types of γ' precipitates, entitled as quenching γ', primary cooling γ' and secondary cooling γ', were identified and their respective precipitation conditions and mechanisms were also discussed. According to the composition gradient across the γ/γ' interfaces and the γ' composition features, the separation mode of these γ' was determined to via the classical nucleation and growth mechanism. In addition, the effects of the γ' forming elements on the nucleation and growth processes of the different generations of γ' were evaluated. It indicates that the diffusion of Ti dominated the primary nucleation while that of Al reigned the following growth and the secondary nucleation.

A Graph Reinforcement Learning Framework for Neural Adaptive Large Neighbourhood Search

Adaptive Large Neighbourhood Search (ALNS) is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 18 years of intensive research into ALNS, the design of an effective adaptive layer for selecting operators to improve the solution remains an open question. In this work, we isolate this problem by formulating it as a Markov Decision Process, in which an agent is rewarded proportionally to the improvement of the incumbent. We propose Graph Reinforcement Learning for Operator Selection (GRLOS), a method based on Deep Reinforcement Learning and Graph Neural Networks, as well as Learned Roulette Wheel (LRW), a lightweight approach inspired by the classic Roulette Wheel adaptive layer. The methods, which are broadly applicable to optimisation problems that can be represented as graphs, are comprehensively evaluated on 5 routing problems using a large portfolio of 28 destroy and 7 repair operators. Results show that both GRLOS and LRW outperform the classic selection mechanism in ALNS, owing to the operator choices being learned in a prior training phase. GRLOS is also shown to consistently achieve better performance than a recent Deep Reinforcement Learning method due to its substantially more flexible state representation. The evaluation further examines the impact of the operator budget and type of initial solution, and is applied to problem instances with up to 1000 customers. The findings arising from our extensive benchmarking bear relevance to the wider literature of hybrid methods combining metaheuristics and machine learning.

Ensemble Inequivalence in Long-Range Quantum Systems.

Ensemble inequivalence, i.e., the possibility of observing different thermodynamic properties depending on the statistical ensemble which describes the system, is one of the hallmarks of long-range physics, which has been demonstrated in numerous classical systems. Here, an example of ensemble inequivalence of a long-range quantum ferromagnet is presented. While the T=0 microcanonical quantum phase-diagram coincides with that of the canonical ensemble, the phase diagrams of the two ensembles are different at finite temperature. This is in contrast with the common lore of statistical mechanics of systems with short-range interactions where thermodynamic properties are bound to coincide for macroscopic systems described by different ensembles. The consequences of these findings in the context of atomic, molecular, and optical setups are delineated.

Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond

A thermal interpretation of the stochastic formalism of a slow-rolling scalar field in de Sitter (dS) is given. We construct a correspondence between Hubble patches of dS and particles living in another space called an abstract space. By assuming a dual description of scalar fields and classical mechanics in the abstract space, we show that the stochastic evolution of the infrared part of the field is equivalent to the Brownian motion in the abstract space filled with a heat bath of massless particles. The 1st slow-roll condition and the Hubble expansion are also reinterpreted in the abstract space as the speed of light and a transfer of conserved energy, respectively. Inspired by this, we sketch quantum emergent particles, which may realize the Hubble expansion by an exponential particle production. This gives another meaning of dS entropy as entropy per Hubble volume.

Correlated qubit coherences stimulated by thermal energy

Abstract Quantum coherence, the ability of a system to be in a quantum superposition of pure states, is a distinct feature of quantum mechanics that has no direct analog in classical mechanics. Quantum states that possess coherence efficiently outperform their classical counterparts in fundamental science and practical applications, including quantum metrology, computation, and simulation. Generation of coherence without the need to employ strong classical drives remains a challenging and not yet experimentally explored task. Beyond individual thermally-induced coherences already proposed for different experiments, correlated quantum coherences of multiple qubits represent a new target. We prove that correlated qubit coherence emerges thermally stimulated from incoherent states in hybrid superconducting and solid-state systems comprising non-interacting qubits coupled only via Dicke-type interaction to a shared thermal mechanical oscillator, exhibits coherences beyond the Tavis–Cummings coupling and, moreover, can be advantageous in quantum sensing.

Simulation of the impact of an ultrasonic drill as a composition of a robotic platform for investigation of soil on celestial bodies

The article discusses the theoretical issues of developing an ultrasonic drill for drilling soil on celestial bodies as part of a robotic platform and formulates the tasks of its control. The specifics of using the drill require a wide temperature range during operation, low energy consumption, an efficient operating cycle and the requirement to ensure the preservation of the structure and composition of the soil when exposed to the tool. One of the promising areas of development is devices with vibration decoupling from the ground by ultrasound due to the transformation of ultrasonic vibrations into repeated impacts of sound frequency using a specially introduced “free” body between the ultrasonic and impact parts of the drill (bit). This allows continuous drilling regardless of the condition of the impact bit, including jamming. The purpose of the work is to select the most effective drill design and compile a mathematical model that provides simulation modeling. Materials and methods. Technical solutions of both domestic and foreign authors were considered, and a prototype was selected. Theoretical works were analyzed and it was found that the materials presented in them do not contain detailed mathematical models necessary for simulation modeling at the stage of design and optimization of the structure. In the theoretical part of the article, mathematical models are proposed, obtained on the basis of equivalent parameters found from a distributed description of the drill design elements. Methods of mathematical physics, classical mechanics and similarity theory were used. The results are that two alternative mathematical models are developed. One of the models has a continuous description with a significantly nonlinear rigidity of the “wall” upon impact, while the impact motion is considered as a type of self-oscillation. The second model is based on the theory of impact. Conclusion. A parametric study was carried out and the dependences of the oscillation frequency of a free body on the size of the impact gap, body mass and amplitude of oscillations of the concentrator, etc. were obtained. The considered models can be used for simulation modeling when developing a drill design. The tasks of controlling a robotic drilling platform are formulated from the position of ensuring the operability of the drill when drilling various soils.

A formulation of quantum fluid mechanics and trajectories

A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics, describing both fluid flow and point mass trajectories. The familiar equations of energy, motion, and those of Lagrangian mechanics are obtained. An energy and continuity equation is demonstrated to be equivalent to the real and imaginary parts of the time dependent Schrödinger equation, respectively, where the Schrödinger equation is in density matrix form. For certain stationary states, using Lagrangian mechanics and a Hamiltonian function for quantum mechanics, equations for point-mass trajectories are obtained. For 1-body states and fluid flows, the energy equation and equations of motion are the Bernoulli and Euler equations of fluid mechanics, respectively. Generalizations of the energy and Euler equations are derived to obtain equations that are in the same form as they are in classical mechanics. The fluid flow type is compressible, inviscid, irrotational, with the nonclassical element of local variable mass. Over all space mass is conserved. The variable mass is a necessary condition for the fluid flow to agree with the zero orbital angular momentum for s states of hydrogen. Cross flows are examined, where velocity directions are changed without changing the kinetic energy. For one-electron atoms, the velocity modification gives closed orbits for trajectories, and mass conservation, vortexes, and density stratification for fluid flows. For many body states, under certain conditions, and by hypotheses, Euler equations of orbital-flows are obtained. One-body Schrödinger equations that are a generalization of the Hartree–Fock equations are also obtained. These equations contain a quantum Coulomb’s law, involving the 2-body pair function of reduced density matrix theory that replace the charge densities.

Quantum-like states on complex synchronized networks

Recent work has exposed the idea that interesting quantum-like (QL) probability laws, including interference effects, can be manifest in classical systems. Here, we propose a model for QL states and QL bits. We suggest a way that huge, complex systems can host robust states that can process information in a QL fashion. Axioms that such states should satisfy are proposed. Specifically, it is shown that building blocks suited for QL states are networks, possibly very complex, that we defined based on k -regular random graphs. These networks can dynamically encode a lot of information that is distilled into the emergent states we can use for QL processing. Although the emergent states are classical, they have properties analogous to quantum states. Concrete examples of how QL functions are possible are given. The possibility of a ‘QL advantage’ for computing-type operations and the potential relevance for new kinds of function in the brain are discussed and left as open questions.