Classical Dynamics Research Articles

On a new class of non-dynamical ABCD algebras for classical and quantum integrable systems

We consider classical and quantum non-dynamical quadratic abcd Lax algebras with classical and quantum gl(n)⊗gl(n)-valued abcd-tensors satisfying a set of quadratic non-dynamical Yang-Baxter-type equations generalizing those of Fredel and Maillet [1]. We establish a relation of some of these equations with the so-called “semi-dynamical” Yang-Baxter equations of [2]. We show that the linearization of the corresponding quadratic structures lead to linear tensor structures with the classical gl(n)⊗gl(n)-valued r-matrices satisfying usual “permuted” classical Yang-Baxter equations [1,3–5]. We consider example of our construction associated with the deformed Zn-graded r-matrix of [10–12] and explicitly construct the corresponding abcd-tensors — both classical and quantum. Small n examples are also considered in some details.

Why the action?

In this note, I present two variations of the principle of stationary action in order to provide alternative ways for students to think about the action that they may find more intuitive than the traditional approach. These methods involve Lagrange multiplier techniques and are, therefore, best suited for students who are encountering the stationary action principle for a second or third time, perhaps in an advanced undergraduate mathematical methods course or a graduate classical mechanics course.

On cat–human interaction from the viewpoint of physics: An equation of motion

This paper provides an enjoyable example through which several concepts of classical mechanics can be understood. We introduce an equation that models the motion of a cat in the presence of a person. The cat is considered as a point particle moving in a potential induced by the person. We demonstrate that this approach to the problem reproduces characteristic behaviors of these curious animals. For instance, the fact that cats do not typically come when they are called, or that they remain longer on the lap of their favorite person; even “zoomies” are reproduced (cats randomly run back and forth across the house). We use this model problem to explore topics of current research such as stochastic equations and periodically driven systems. The pedagogical value of this work and its potential use in teaching are discussed.

Federated Learning for Personalized Financial Recommendations

Abstract: Federated Learning (FL) has been the solution to one of those biggest contributors that have scared us from using Machine learning, i.e. Privacy [ for sensitive domains like finance ]. This survey focuses on leveraging Federated Learning in creating personalized recommendation systems for financial products such as loans, investment plans, credit cards and savings. For example, classical recommendation systems usually work in a centralized way to store a lot of sensitive financial data (or derivative structures), this setting presents other well-known privacy issues and security risks. FL provides a solution that enables multiple financial institutions to work together to train a global recommendation model without the need any of them to share their raw customer data. The paper reviews federated learning, and some key take ways are on differential privacy and secure aggregation to protect customer data while improving the quality of recommendations. We also talk about how to solve some problems like heterogeneity of the data, model convergence and regulatory constraints required in financial methods. The paper concludes by detailing future directions for federated learning in finance, with focus on how personalized financial recommendations can be dramatically transformed while preserving user privacy.

Uncovering the Secrets of Motion: A Literature Review of Lagrange and Newtonian Mechanics

Physics is a branch of natural science. Since ancient times, humans have been interested in the movement of objects around them and motion is an area studied in mechanics. This research aims to understand the principles of mechanics in Lagrange and Newtonian mechanics for solving motion problems and their applications. The method used is the literature review method. Literature is a comprehensive overview of previous research on a particular topic. Literature review is a systematic process for identifying, evaluating, and synthesizing previously published scientific works on a particular topic. There are 20 sources used, consisting of books and scientific journals. The research results show that motion is an object that experiences movement from one place to another. Problems of motion of objects can be solved using the laws and principles of Newtonian and Lagrange mechanics. Lagrange mechanics is used to solve complex problems that cannot be solved with Newtonian mechanics. Lagrange mechanics focuses on the forces that cause objects to move, while Newtonian mechanics focuses on the energy that causes objects to move.

Classical entanglement and entropy

Motivated by recent discussions of entanglement in the context of high energy scattering, we consider the relation between the entanglement entropy of a highly excited state of a quantum system and the classical entanglement entropy of the corresponding classical system. We show on the example of two weakly coupled harmonic oscillators that the two entropies are equal. Quantum mechanically, the reduced density matrix which yields this entropy is close to the maximally entangled state. We thus observe that the nature of entanglement in this type of state is purely classical.

Entropy Considerations in Stochastic Electrodynamics

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations that have been fully carried out to date are discussed in two main cases: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh–Jeans radiation; and second, where only these radiation fields exist within a cavity. The emphasis here is on the first, more complicated, case, where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in classical statistical mechanics, involving probabilistic notions of phase-space occupation, the calculations to date for both particles and fields, or for fields alone, follow the caloric entropy method, where the notions of heat flow, adiabatic surfaces, and isothermal conditions are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have successfully gone.

THOUGHT EXPERIMENT ANALYSES OF ALBERT EINSTEIN'S ELEVATOR

In this contribution we identify, analyze and interpret Einstein's elevator as a paradigmatic thought experiment (TE) that shows how modern physics may surpass classical mechanics. On surface analyses we show that Einstein’s elevator is, in fact, a series of interrelated TE, TE1 through TE6, involving two frames of reference – or two systems of coordinates, K and K', deducing principle of relativity from Galileo – and two observers, an inside and outside observer. On deep analyses of Einstein's elevator appears a deconstructive TE featuring principle of relativity, destructing, falsifying Newton's theory, that does not hold on to principle of relativity, and constructing, verifying Einstein's, that does. On interpretation, admitting theoretical TE may have flaws as with regard to imaginability, conceptual and terminological coherence, we argue that TE are usually valid as arguments, and are rather considered antifallacies than fallacies. TE may develop on analysis from prima facie or secunda facie (in)conceivability to ideal (in)conceivability; our logical analyses validate Einstein’s elevator as a paradigmatic TE. Lastly, we may add two 21st-century conditions to (e.g. Karl Popper's) view of growth of science –global cross-culturalism and environmental pragmaticism– to arrive at a balanced view of progress of science and society1.

Hybridization of Learning Techniques and Quantum Mechanism for IIoT Security: Applications, Challenges, and Prospects

This article describes our point of view regarding the security capabilities of classical learning algorithms (CLAs) and quantum mechanisms (QM) in the industrial Internet of Things (IIoT) ecosystem. The heterogeneity of the IIoT ecosystem and the inevitability of the security paradigm necessitate a systematic review of the contributions of the research community toward IIoT security (IIoTsec). Thus, we obtained relevant contributions from five digital repositories between the period of 2015 and 2024 inclusively, in line with the established systematic literature review procedure. In the main part, we analyze a variety of security loopholes in the IIoT and categorize them into two categories—architectural design and multifaceted connectivity. Then, we discuss security-deploying technologies, CLAs, blockchain, and QM, owing to their contributions to IIoTsec and the security challenges of the main loopholes. We also describe how quantum-inclined attacks are computationally challenging to CLAs, for which QM is very promising. In addition, we present available IIoT-centric datasets and encourage researchers in the IIoT niche to validate the models using the industrial-featured datasets for better accuracy, prediction, and decision-making. In addition, we show how hybrid quantum-classical learning could leverage optimal IIoTsec when deployed. We conclude with the possible limitations, challenges, and prospects of the deployment.

Incipient Fault Detection for the Spindle Bearing of a Cement Grinding Machine based on Vibrational Resonance

Abstract The spindle bearing of a circulation fan is an important component of a cement grinding machine. In addition to the faults on the spindle bearing, impeller wear and ash accumulation may cause dynamic unbalance and complex vibration interference as noise, which decreases the accuracy of fault detection based on vibrational signals and traditional signal processing-based methods at the early stage of a bearing fault. To address this issue, this paper presents a new fault detection method for the spindle bearing by utilizing extra injected noise and vibrational resonance. To enhance the fault signature and resonance performance, the nonlinear system of the traditional vibrational resonance is replaced by a new hybrid steady-state system, and the underdamped term is considered in the new system. The proposed system provides more possibilities to achieve resonance by adjusting the system parameters and overcomes the limitations of output saturation caused by the classical bistable system. The proposed method is validated by analysing the collected vibration signals from a spindle bearing of a circulation fan in practice and is compared with other noise-elimination fault detection methods. The results demonstrate the effectiveness and superior performance of the proposed method.

A Frustrated Antipolar Phase Analogous to Classical Spin Liquids.

The study of magnetic frustration in classical spin systems is motivated by the prediction and discovery of classical spin liquid states. These uncommon magnetic phases are characterized by a massive degeneracy of their ground state implying a finite magnetic entropy at zero temperature. While the classical spin liquid state is originally predicted in the Ising triangular lattice antiferromagnet in 1950, this state has never been experimentally observed in any triangular magnets. The discovery of an electric analogue of classical spin liquids on a triangular lattice of uniaxial electric dipoles in EuAl12O19 is reported here. This new type of frustrated antipolar phase is characterized by a highly-degenerate state at low temperature implying an absence of long-range antiferroelectric order, despite short-range antipolar correlations. Its dynamics are governed by a thermally activated process, slowing down upon cooling toward a complete freezing at zerotemperature.

Viewing the cat as a point particle

A model of cat-human interactions provides a useful and enjoyable example for teaching classical mechanics.

Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation

Abstract We report on the theoretical and experimental investigation of the transition of a typical quantum system with mixed regular-integrable classical dynamics to one with violated time-reversal (T) invariance. The measurements are performed with a flat superconducting microwave resonator with circular shape in which chaoticity is induced by using either long antennas or inserting two circular disks into the cavity, and by magnetizing a ferrite disk placed at its center, which leads to violation of T invariance. We propose an extension of the Rosenzweig-Porter (RP) model, which interpolates between mixed regular-chaotic instead of integrable dynamics and fully chaotic dynamics with violated T-invariance, and derive a Wigner-surmise like analytical expression for the corresponding nearest-neighbor spacing distribution. We propose a procedure involving this result and those for the RP model to determine the size of T-invariance violation and chaoticity and validate it employing the experimental eigenfrequency spectra.

Classicalization of Quantum Mechanics: Classical Radiation Damping Without the Runaway Solution

In this paper, we review a new treatment of classical radiation damping, which resolves a known contradiction in the Abraham–Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicalizing quantum mechanics by replacing the canonical commutation relation from quantum mechanics with the Poisson bracket relation in classical mechanics.

Quantum and classical dynamics correspondence and the brachistochrone problem

Quantum and classical dynamics correspondence and the brachistochrone problem

Uncovering Holistic Contemporary Paradigms and Hamemayu Hayuning Bawana to Realise Sustainable Development Goals

Objective: This research aims to: (1) understand the historical development of Holistic Contemporary Worldview (CHW) and Kejawen Philosophy (Hamemayu Hayuning Bawana/HHB); (2) explore the correlation between CHW and HHB; (3) compare the axiology of HHB and CHW to better understand the path to achieving sustainable development goals; and (4) identify opportunities for maintaining sustainability through the perspectives of CHW and HHB. Theoretical Framework: The Earth is currently facing unsustainable changes, which are evident in climate change and the increasing frequency of disasters. These problems are believed to stem from reductionist-mechanist thinking, which fosters an anthropocentric attitude. In contrast, holistic thinking offers a new perspective on nature, seeing it as an interconnected whole where each component supports the others to maintain prosperity and balance. This idea is in line with the Javanese philosophy of life, HHB, which emphasizes harmony between humans and nature to enhance the beauty of life. Both concepts highlight the need for fundamental changes in the way humans interact with each other and nature to support the achievement of Sustainability especially the implementation of the Sustainable Development Golas (SDGs). Method: This descriptive qualitative research uses a literature study technique that is conducted in three stages. First, a literature study on the historical development of human views on nature, both from the Western view (CHW) and the Eastern view, especially Java (Kejawen-HHB). These historical developments are presented in the form of narratives to provide a clear picture of events and context, thus helping in understanding each philosophy. The second stage reviews these narratives to identify the core similarities and differences between the two approaches. Finally, the third stage analyses these comparisons to find clues about new approaches to sustainability, especially attitudinal changes to support the achievement of sustainable development goals Results and Discussion: This research shows that the concepts of CHW and HHB are two concepts that emerged from two different regions and times but have the same philosophical line. Both understand that all components of nature need to coexist and respect each other psychologically and even spiritually. This change in attitude is necessary to avoid the evil nature of humans (greed and arrogance) in fulfilling their needs in the form of development. The goal of sustainable development should be utilized for the benefit of the many and the broad (inclusive), which is the core concept of deep ecological understanding (Ecosophy of CHW) and needs to be supported by the concept of roso (spiritual culture of HHB). Both approaches have significant similarities and differences in some aspects but share the common goal of maintaining a dynamic balance to sustain living systems. Research Implications: The findings of this research are expected to contribute to a new perspective on how to achieve sustainability. The old approach based on classical mechanics is still relevant and useful to support the achievement of the SGDs, but the complexity of the world demands a change in behaviour in treating the universe and development. CHW and HHB provide new clues on how to achieve this. Originality/Value: This study compares and correlates two approaches from distinct origins: one rooted in the logic-driven Western culture and the other in the spiritual-based Eastern tradition. These approaches also emerged in different eras: one in the modern, complex age, and the other in the mythology-based ancient kingdom. By examining this correlation, the study underscores the importance of regulating thoughts and behaviors to ensure the continuity of life, particularly within the complexities of modern civilization.

Dynamical analysis and fault detection application of a time-delayed multi-stable stochastic resonance system driven by white correlated noises.

Bearing fault diagnosis is a crucial means to ensure the normal operation of machinery, reduce maintenance costs, enhance equipments safety and extend the service life of bearings. However, the noise interference in input signals often affects the effective extraction of bearing fault signals. In this paper, a time-delay multi-stable stochastic resonance (SR) system driven by white correlated noises is proposed. Firstly, the expressions of the steady-state probability density (SPD) function and the mean first passage time (MFPT) is derived. Simultaneously, we delve into the influences of various system parameters, including multiplicative noise intensity, additive noise intensity, noise correlated strength, time-delay, and time-delay feedback intensity, on the dynamical behavior exhibited by particles within the system. Then, according to the signal-to-noise ratio (SNR) formula, the paper investigates the impact of system parameters on the SNR. It is found that the ease of SR occurrence is directly related to the system parameters. Finally, the experimental results demonstrate that the proposed method exhibits superior performance in detecting faults compared with the classical bistable SR system and the quad-stable SR system.

On the exploration of new solitary wave solutions for the classical integrable Kuralay-IIA system of equations

In this paper, we derive various new optical soliton solutions for the coupled Kuralay-IIA system of equations using an innovative solution approach known as the ϕ 6 − model expansion technique. This solution methodology employs a traveling wave transformation to reduce the considered problem into an easily solvable higher-order ordinary differential equation. Unlike other existing related methods, this solution approach adopted here allows us to extract a rich list of diverse exact soliton solutions for the considered problem. The obtained solutions incorporate the Jacobi elliptic functions which are shown to degenerate into trigonometric and hyperbolic function solutions. These solutions exhibit distinct wave structures consisting of dark, bright, rational, periodic, singular and mixed optical solitons profiles. In exploring the impact of spatial and temporal variables on the wave patterns of the considered model, physical structures of some of the obtained solitons solutions are characterized through 3D, contour and 2D wave profiles for selected parameter values. This not only ensures the validity of the solutions as well as the constraints arising from the solution technique but also offers researchers a deeper understanding of the properties of the considered problem. The outcomes here demonstrate the applicability, versatility and efficiency of the considered solution approach for deriving diverse new soliton solutions for even more complex systems of nonlinear evolution equations.

Understanding of topological mode and skin mode morphing in 1D and 2D non-Hermitian resonance-based meta-lattices

Recent advances have demonstrated that the non-Hermitian skin effect (NHSE), induced by system non-Hermiticity, can manipulate the localization of in-gap topological edge modes (TEMs) within mechanical topological insulators. This study introduces a straightforward analytical framework to elucidate the competition between NHSE and TEM localization in a classical mechanical meta-lattice, highlighting its impact on the dynamic behavior of TEMs within separate Bragg scattering band gaps (BSBGs). We propose a 1D non-Hermitian meta-lattice featuring a locally resonant system with active feedback control, characterized by a real-valued transfer function. This local resonance creates two separate BSBGs, each hosting a TEM defined by non-Hermitian bulk-edge correspondence. Our theoretical and numerical analyses reveal that the NHSE, with its asymmetric localization within the two BSBGs, can shift the localization of TEMs in distinct ways. This leads to an asymmetric phase transition, wherein one TEM can be delocalized and relocalized by tuning the transfer function, while the other maintains its initial localization. Moreover, we extend the mechanism of 1D asymmetric TEM delocalization to the non-Hermitian morphing of TEMs, showcasing notable examples such as temporal and spatial topological wave pumping with space- and time-dependent transfer functions in 1D time-varying and 2D stacked meta-lattices. This research bridges a gap between non-Hermitian mechanical constructs and their potential applications in classical mechanics, reinterpreting known topological wave control in 1D and uncovering new mechanisms in 2D.

Influence of large-scale free-stream turbulence on bypass transition in air and organic vapour flows

The free-stream turbulence (FST) induced transition in perfect and non-ideal gas zero-pressure-gradient flat-plate boundary layers is investigated by means of large-eddy simulations. The study focuses on the influence of large incoming disturbances over the laminar-to-turbulent transition, by comparing two different integral length scales $L_f$ , which differ by a factor of seven, at different FST intensities $T_u$ . High-subsonic dense-gas boundary layers of the organic vapour Novec649, representative of organic Rankine cycle applications, are compared with air flows at Mach numbers 0.1 and 0.9. Compressibility and non-ideal gas effects are shown to be of minor importance in comparison to the influence of the FST integral length scale $L_f$ . An increase of the inlet turbulent intensity always promotes transition, whereas an increase of $L_f$ has a double effect on the transition onset. At $T_u=2.5\,\%$ , increasing $L_f$ promotes the transition, while it tends to delay transition for an FST intensity of 4 %. Larger FST integral scales tend to increase the spanwise distance between laminar streaks generated in the boundary layer. Two competing transition scenarios are observed. When the incoming turbulence intensity and length scale are moderate, the classical bypass route consists in the linear non-modal growth of streaks, which then experience secondary instabilities (sinuous or varicose) and lead to the generation of turbulent spots. The second scenario is characterized by the appearance of $\Lambda$ -shaped structures near the inlet, which are further stretched to hairpin vortices before breaking down to turbulence. Spot inceptions can therefore occur at earlier locations than the streak growth. We are then faced with a competition between the classical bypass transition and nonlinear response mechanisms that ‘bypass’ this route. The present case at high $L_f$ and low $T_u$ is an example of a competing scenario, but even for the higher $T_u$ and $L_f$ conditions, only approximately one-third of turbulent spots are due to the $\Lambda$ -shaped events. The nonlinear alternative route has strong similarities with scenarios described previously in the literature in the presence of leading edge effects or due to passing wakes. Such a path is governed by the turbulence intensity, but also by the integral length scale, with both parameters playing a critical role in the generation of the $\Lambda$ -shaped structures near the inlet. This alternative mechanism is found to be robust under varying flow and thermodynamic conditions.