Physical Systems Research Articles

Analysis of fractional Swift-Hohenberg models using highly accurate techniques within the Caputo operator framework

This investigation aims to analyze and solve the fractional SwiftHohenberg (FSH) equation using the Aboodh residual power series method (ARPSM) and Aboodh transform iterative method (ATIM) within the Caputo operator framework. This equation is widely used in modeling pattern formation phenomena in various physical systems. Thus, the current study focuses on understanding the mechanics and dynamics of wave propagation described by this equation. Additionally, it investigates the impact of the fractional parameter on the behavior of these waves. By employing both ARPSM and ATIM, we aim to obtain highly accurate and efficient approximations to this equation. The effectiveness of these methods is demonstrated through numerical simulations, where we compare the obtained results with existing analytical and numerical solutions. Our findings highlight the utility of the ARPSM and ATIM in studying complex nonlinear fractional differential equations, providing valuable insights into pattern formation dynamics governed by the Swift-Hohenberg equation.

Kolmogorov-Arnold Network Made Learning Physics Laws Simple.

In recent years, contrastive learning has gained widespread adoption in machine learning applications to physical systems primarily due to its distinctive cross-modal capabilities and scalability. Building on the foundation of Kolmogorov-Arnold Networks (KANs) [Liu, Z. et al. Kan: Kolmogorov-arnold networks. arXiv 2024, 2404.19756], we introduce a novel contrastive learning framework, Kolmogorov-Arnold Contrastive Crystal Property Pretraining (KCCP), which integrates the principles of CLIP and KAN to establish robust correlations between crystal structures and their physical properties. During the training process, we conducted a comparative analysis between Multilayer Perceptron (MLP) and KAN, revealing that KAN significantly outperforms MLP in both accuracy and convergence speed for this task. By extending the capabilities of contrastive learning to the realm of physical systems, KCCP offers a promising approach for constructing cross-data structural and cross-modal physical models, representing an area of considerable potential.

Cascading tipping points of Antarctica and the Southern Ocean.

Antarctica and the Southern Ocean are key elements in the physical and biological Earth system. Human-induced climate change, and other human activities in the region, are leading to several potential interacting tipping points with major and irreversible consequences. Here, we examine eight potential physical, biological, chemical, and social Antarctic tipping points. These include ice sheets, ocean acidification, ocean circulation, species redistribution, invasive species, permafrost melting, local pollution, and the Antarctic Treaty System. We discuss the nature of each potential tipping point, its control variables, thresholds, timescales, and impacts, and focus on the potential for cumulative and cascading effects as a result of their interactions. The analysis provides substantial evidence of the need for more concerted and rapid action to limit climate change and to minimise the impacts of local human activities to avoid these cascading tipping points.

Quantum Advantages in (n, d) →1 Random Access Codes

Abstract A random access code (RAC), corresponding to a communication primitive with various applications in quantum information theory, is an instance of a preparation-and-measurement scenario. In this work, we consider (n, d)-RACs constituting an n-length string, constructed from a d size set of letters, and send an encoding of the string in a single d-level physical system and present their quantum advantages. We first characterize optimal classical RACs and prove that a known classical strategy, the so-called majority-encoding-identity-decoding, is optimal. We then construct a quantum protocol by exploiting only two incompatible measurements (the minimal requirement) and show the advantages beyond the classical one. We also discuss the generality of our results and whether quantum advantages are valid for all types of (n, d)→1 RACs.

Educational Cyber–Physical Systems (ECPSs) for University 4.0

University 4.0 represents the adaptation of the Education 4.0 paradigm to the university context. The core principle is the automated supervision of the entire student learning process by an AI-driven computer assistant, allowing for timely adjustments based on the student’s progression. Critical to this process is the assistant’s ability to collect comprehensive information on all student activities within the curriculum, particularly overseeing pedagogical activities in real time to make necessary adaptations. This utilizes Educational Cyber–Physical Systems (ECPSs) to gather all relevant data and extract appropriate information effectively. This article examines a specific case of practical work involving students at two distinct geographical locations collaborating in a blended learning environment. A specialized ECPS is deployed to collect data from equipment at both sites, enabling the modeling of the pedagogical sequence, the cyber–physical system, and the data necessary for monitoring student progress in real time.

Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians

Quantum and classical systems evolving under the same formal Hamiltonian H may exhibit dramatically different behavior after the Ehrenfest timescale tE∼log(ħ-1), even as ħ→0. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution. Its classical counterpart is given by the Fokker–Planck equation on phase space, which describes Hamiltonian flow with friction and diffusive noise. The quantum and classical evolutions may be compared via the Wigner-Weyl representation. Due to decoherence, they are conjectured to match closely for times far beyond the Ehrenfest timescale as ħ→0. We prove a version of this correspondence, bounding the error between the quantum and classical evolutions for any sufficiently regular Hamiltonian H(x, p) and Lindblad functions Lk(x,p). The error is small when the strength of the diffusion D associated to the Lindblad functions satisfies D≫ħ4/3, in particular allowing vanishing noise in the classical limit. Our method uses a time-dependent semiclassical mixture of variably squeezed Gaussian states. The states evolve according to a local harmonic approximation to the Lindblad dynamics constructed from a second-order Taylor expansion of the Lindbladian. Both the exact quantum trajectory and its classical counterpart can be expressed as perturbations of this semiclassical mixture, with the errors bounded using Duhamel’s principle. We present heuristic arguments suggesting the 4/3 exponent is optimal and defines a boundary in the sense that asymptotically weaker diffusion permits a breakdown of quantum-classical correspondence at the Ehrenfest timescale. Our presentation aims to be comprehensive and accessible to both mathematicians and physicists. In a shorter companion paper, we treat the special case of Hamiltonians that decompose into kinetic and potential energy with linear Lindblad operators, with explicit bounds that can be applied directly to physical systems.

Effective dimensionality of space-time in f(R)-general relativity with quantum boundary terms included

I study an extended theory of General Relativity that incorporates normalized relativistic velocities, where the boundary terms in the varied f(R)-action are considered as a part of the physical system to be studied. Within this context, I investigate how the classical perturbations can be originated by quantum geometric perturbations, that alters the dynamics of the physical system without perturbations. To do it we use a modified nonlinear quantum algebra recently introduced. The quantum field perturbations of space-time also alter the geodesic equations that describe the dynamics of the relativistic velocities, the metric tensor and the Ricci tensor. But perhaps the most intriguing of this phenomena is that these space-time alterations change the effective number of space-time dimensions of the system with perturbations included N(z), in a such manner that N(z) can take an irrational value N(z=2)=8/(1+5)≃2.4721, when the nonlinear quantum perturbations of space-time are related to the relativistic velocities U¯μ. To illustrate the theory, we calculate exactly the cosmological parameter in an early inflationary universe.

Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system

Abstract In this study, we conduct a comprehensive investigation of the novel characteristics of the (2 + 1)-dimensional stochastic Hirota–Maccari System (SHMS), which is a prominent mathematical model with significant applications in the field of nonlinear science and applied mathematics. Specifically, SHMS plays a critical role in the study of soliton dynamics, nonlinear wave propagation, and stochastic effects in complex physical systems such as fluid dynamics, optics, and plasma physics. In order to account for the abrupt and significant fluctuation, the aforementioned system is investigated using a Wiener process with multiplicative noise in the Itô sense. The considered equation is studied by the new extended direct algebraic method (NEDAM) and the modified Sardar sub-equation (MSSE) method. By solving this equation, we systematically derived the novel soliton solutions in the form of dark, dark-bright, bright-dark, singular, periodic, exponential, and rational forms. Additionally, we also categorize and analyze the W-shape, M-shape, bell shape, exponential, and hyperbolic soliton wave solutions, which are not documented by researchers. The bifurcation, chaos and sensitivity analysis has been depicted which represent the applicability of the system in different dynamics. These findings greatly advance our knowledge of nonlinear wave events in higher-dimensional stochastic systems both theoretically and in terms of possible applications. These findings are poised to open new avenues for future research into the applicability of stochastic nonlinear models in various scientific and industrial domains.

Application of Natural Transform Decomposition Method for Solution of Fractional Richards Equation

This study employs the natural transform decomposition method (NTDM) to examine analytical solutions of the nonlinear time-fractional Richards equation (TFRE). The NTDM is an innovative and attractive hybrid integral transform strategy that elegantly combines the Adomian decomposition method and the natural transform method. This solution strategy effectively generates rapidly convergent series-type solutions through an iterative process involving fewer calculations. The convergence and uniqueness of the solutions are presented. To demonstrate the efficiency of the considered solution method, two test cases of the TFRE are investigated within the framework of the Caputo-Fabrizio and Atangana-Baleanu-Caputo derivatives whose definitions incorporate nonsingular kernel functions. Numerical comparisons between the obtained approximate solutions, exact solutions, and those from existing related literature are presented to show the validity and accuracy of the technique. Graphical representations demonstrating the effect of varying non-integer, temporal, and spatial parameters on the behavior of the obtained model solutions are also presented. The results indicate that the execution of the method is straightforward and can be employed to explore complex physical systems governed by time-fractional nonlinear partial differential equations.

From Traditional to Transformational: Leveraging Digital Twins for Advanced Testing in Life Insurance

The Life Insurance industry is undergoing a profound digital transformation, transitioning from traditional, static methodologies to agile, data-intelligent ecosystems capable of adapting to dynamic customer demands and stringent regulatory complexities. At the forefront of this shift is the adoption of digital twins—high- fidelity virtual replicas of physical systems, processes, and assets—specifically for testing and optimizing Life Insurance platforms. This paper provides a deep dive into the role of Digital twins in the Life Insurance domain, exploring their powerful applications in underwriting, policy lifecycle management, and claims processing. By accurately simulating complex, real-world scenarios, Digital twins enable predictive testing environmentsthat refine system resilience, preemptively identify risk exposures, and ensure operational continuity. Through this sophisticated digital infrastructure, insurers gain a transformative tool for enhancing precision, boosting reliability, and driving efficiency in core insurance processes. This research investigates the architecture, applications, and strategic trajectory of Digital twins as next generation testing mechanisms reshaping Life Insurance. Keywords: Digital Twin, Life Insurance, Underwriting, Policy Lifecycle Management, Claims Processing, Virtual Simulation, System Resilience, Operational Efficiency, Data-Driven Testing, Digital Transformation, Predictive Modeling, Testing Framework, Real-World Scenarios

Design of Public Physical Education Curriculum Quality Evaluation System Based on the “5V” Characteristics of Computer Big Data

In order to improve the teaching effect of public physical education courses to the greatest extent and lay the foundation for the process of teaching reform, this paper puts forward the design of a public physical education course quality evaluation system based on the “5V” characteristics of computer big data. Analyze the characteristics of big data “5V” and study its application in public physical education courses; analyze the action estimation, prior, and update, failure recovery of public physical education course teaching, and get the three-dimensional visual positioning result of public physical education course teaching; collect the upper arm action image, extract the upper arm action image contour feature through edge contour detection, analyze the contour feature error characteristics, obtain the pixel component weighted value of the contour feature, further obtain the fuzzy error value of the upper arm action image contour feature through calculation, and according to the fuzzy error value, the design of public physical education course quality evaluation system is completed. The experimental results show that the average error recognition accuracy of the research method is 99.63%. The class hours are adjusted according to the proportion of disciplines, and the corresponding teaching plan is formulated. The accuracy of recommending internship posts for students is relatively high.

Physical conditions in the analytical solution on the Mathieu equation

The study aims to analyze the Mathieu equation associated with linear systems under properties, use the one-dimensional Floquet theorem and explain the behavior of the solutions of the Mathieu equation and function relating to the Hill equation together with the theory of disturbances. The most common mathematical problem in physics is finding solutions to certain second-order differential equations subject to boundary conditions. A hypothetical deductive approach method, handling qualitative equations of mathematical physics, was adopted in review. With Mathieu's equation, the existence of the physical conditions that influence the value of the parameters that define the equation were answered. It is important due to its usefulness in the field of analytical and mechanical dynamics, physical systems subjected to parametric excitation; In addition, it leaves other variations open for new applications.

Neuroadaptive Control of a Continuum Robot for Finger Rehabilitation

This study has designed an easy-to-wear parallel continuum robot-based hand rehabilitation system that supports and enhances the finger’s flexion, extension, abduction, and adduction movements. The primary novelty of the proposed system lies in its ability to focus therapeutic exercises on a single joint, a feature not commonly found in existing rehabilitation robots. A kinematic model of the system was developed, and to perform both kinematic and dynamic analyses, a multibody model was constructed in the MATLAB Simulink environment. Joint angle control was implemented using a nominal controller, and to account for individual uncertainties in joint dynamics, a neuroadaptive controller was integrated with the nominal controller. This approach aims for the neural network architecture to learn these uncertainties during control iterations and incorporate them into the control, resulting in a robust controller. Thus, a model reference control approach was proposed for active and passive rehabilitation processes. The system model was tested in a simulation environment, and then all tests were repeated in the physical system. The simulation and real system results include the real system’s open-loop responses, nominal controller responses for each joint, responses, and the results for active, passive, and assistive control modes.

Building a Digital Twin for a Ground Heat Exchanger

AbstractThis research investigates the development of a digital twin (DT) for ground heat exchangers (GHEs) and its potential to enhance the efficiency and sustainability of shallow geothermal energy systems. It introduces an innovative approach for building a GHE‐DT that connects the physical and digital systems to monitor key parameters, predict issues, and optimize energy efficiency. The process involves several phases including implicit knowledge codification, data‐driven analysis, model construction, and system design. The study emphasizes real‐time monitoring of the effective parameters: ground temperature and fluid conditions (flow rate, temperature, and pressure). The GHE‐DT's digital system mainly comprises three sections, namely, data storage, mathematical modeling, and data‐driven modeling. The role of the presented mathematical model is to simulate the GHE's behavior and assess its performance characteristics, such as the heat exchanger's effectiveness and efficiency. Additionally, the data‐driven model used in the proposed DT utilizes formal concept analysis and relation concept analysis to identify connections and associations among parameters for a better understanding of the GHE functioning. The GHE‐DT provides useful services including trend analysis, problem prediction, and correlation analysis. These services provide engineers and operators with the opportunity to increase dependability, save maintenance costs, and optimize GHE performance.

Algebraic structures formalizing the logic of effect algebras incorporating time dimension

Abstract Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the corresponding events. It is natural to ask how to introduce the logical connective implication in effect algebras. For lattice-ordered effect algebras this task was already solved by several authors, including the present ones. We concentrate on effect algebras that need not be lattice-ordered since these can better describe the events occurring in the quantum physical system. Although an effect algebra is only partial, we try to find a logical connective implication which is everywhere defined. But such a connective can be “unsharp” or “inexact” because its outputs for given pairs of entries need not be elements of the underlying effect algebra, but may be subsets of (mutually incomparable) maximal elements. We introduce such an implication together with its adjoint functor representing conjunction. Then we consider so-called tense operators on effect algebras. Of course, also these operators turn out to be “unsharp” in the aforementioned sense, but they are in a certain relation with the operators implication and conjunction. Finally, for given tense operators and given time set T, we describe two methods how to construct a time preference relation R on T such that the given tense operators are either comparable with or equivalent to those induced by the time frame (T, R).

Digital Twin-Based Smart Feeding System Design for Machine Tools

With the continuous development of intelligent manufacturing technology, the application of intelligent feed systems in modern machine tools is becoming increasingly widespread. Digital twin technology achieves the monitoring and optimization of the entire life cycle of a physical system by constructing a virtual image of the system, while neural network controllers, with their powerful nonlinear fitting ability, can accurately capture and simulate the dynamic behavior of complex systems, providing strong support for the optimization control of intelligent feed systems. This article discusses the design and implementation of an intelligent feed system based on digital twins and neural network controllers. Firstly, this article establishes a mathematical model based on the traditional ball screw structure and analyzes the dynamic characteristics and operating mechanism of the system. Subsequently, the mathematical model is fitted using a neural network controller to improve control accuracy and system response speed. The experimental results demonstrate that the neural network controller shows good consistency in fitting traditional mathematical models, not only effectively capturing the nonlinear characteristics of the system but also maintaining stable control performance under complex operating conditions.

High-dimensional anticounterfeiting nanodiamonds authenticated with deep metric learning

Physical unclonable function labels have emerged as a promising candidate for achieving unbreakable anticounterfeiting. Despite their significant progress, two challenges for developing practical physical unclonable function systems remain, namely 1) fairly few high-dimensional encoded labels with excellent material properties, and 2) existing authentication methods with poor noise tolerance or inapplicability to unseen labels. Herein, we employ the linear polarization modulation of randomly distributed fluorescent nanodiamonds to demonstrate, for the first time, three-dimensional encoding for diamond-based labels. Briefly, our three-dimensional encoding scheme provides digitized images with an encoding capacity of 109771 and high distinguishability under a short readout time of 7.5 s. The high photostability and inertness of fluorescent nanodiamonds endow our labels with high reproducibility and long-term stability. To address the second challenge, we employ a deep metric learning algorithm to develop an authentication methodology that computes the similarity of deep features of digitized images, exhibiting a better noise tolerance than the classical point-by-point comparison method. Meanwhile, it overcomes the key limitation of existing artificial intelligence-driven classification-based methods, i.e., inapplicability to unseen labels. Considering the high performance of both fluorescent nanodiamonds labels and deep metric learning authentication, our work provides the basis for developing practical physical unclonable function anticounterfeiting systems.

A blockchain consensus mechanism for real-time regulation of renewable energy power systems

With the ongoing development of renewable energy sources, information technologies and physical energy systems are further integrated, which leads to challenges in ensuring the secure and stable operation of renewable energy power systems in the face of potential cyber threats. The strengths of blockchain in cybersecurity make it a promising solution to these challenges. However, existing blockchains are not well-suited for control tasks due to their low real-time performance. Here, we present a consensus mechanism that enables real-time security control of systems, called Proof of Task. Instead of solving meaningless hash puzzles in Proof of Work, Proof of Task addresses problems closely related to the stable operation and control performance of these systems. With the proposed verification mechanism, Proof of Task significantly enhances the real-time performance of blockchain while mines its computational resources for tasks of interest. To demonstrate the effectiveness and necessity of Proof of Task, it is deployed across three renewable energy power systems. The results show that Proof of Task markedly fortifies the security and computing capability of these systems, ensuring their reliable and stable operation. This work highlights the promise of blockchain to facilitate security control and trusted computing of large-scale, complex-dynamic systems.

Hyperbolic Non-Polynomial Spline Approach for Time-Fractional Coupled KdV Equations: A Computational Investigation

The time-fractional coupled Korteweg–De Vries equations (TFCKdVEs) serve as a vital framework for modeling diverse real-world phenomena, encompassing wave propagation and the dynamics of shallow water waves on a viscous fluid. This paper introduces a precise and resilient numerical approach, termed the Conformable Hyperbolic Non-Polynomial Spline Method (CHNPSM), for solving TFCKdVEs. The method leverages the inherent symmetry in the structure of TFCKdVEs, exploiting conformable derivatives and hyperbolic non-polynomial spline functions to preserve the equations’ symmetry properties during computation. Additionally, first-derivative finite differences are incorporated to enhance the method’s computational accuracy. The convergence order, determined by studying truncation errors, illustrates the method’s conditional stability. To validate its performance, the CHNPSM is applied to two illustrative examples and compared with existing methods such as the meshless spectral method and Petrov–Galerkin method using error norms. The results underscore the CHNPSM’s superior accuracy, showcasing its potential for advancing numerical computations in the domain of TFCKdVEs and preserving essential symmetries in these physical systems.

Optimizing operations of flexible assembly systems: demonstration of a digital twin concept with optimized planning and control, sensors and visualization

AbstractThis paper presents the development of an optimized planning and control method for flexible manufacturing and assembly systems. While the significant potential of flexible manufacturing concepts to help producers adapt to market developments is recognized, the complexity of the flexible systems and the need to optimally plan and control them is a major obstacle in their practical implementation. Thus, this paper aims to develop a comprehensive digital planning method, based on a digital twin and to demonstrate the feasibility of the approach for practical application scenarios. The approach consists of four modules: (1) a simulation-based optimization module that applies reinforcement learning and genetic algorithms to optimize the module configuration and job routing in cellular reconfigurable manufacturing systems; (2) a synchronization module that links the physical and virtual systems via sensors and event handling; (3) a sensor module that enables a continuous status update for the digital twin; and (4) a visualization module that communicates the optimized plans and control measures to the shop floor staff. The demonstrator implementation and evaluation are implemented in a learning factory. The results include solutions for the method components and demonstrate their successful interaction in a digital twin, while also pointing towards the current technology readiness and future work required to transfer this demonstrator implementation to a full-scale industrial implementation.