Dynamics Of Physical Systems Research Articles

A novel approach to construct optical solitons solutions of complex Ginzburg–Landau equation with five distinct forms of nonlinearities

This paper presents a recently introduced innovative approach for analyzing closed-form solutions of nonlinear partial differential equations. While various methods exist for deriving closed-form solutions to many nonlinear evolution equations, additional solutions are still needed to study the various dynamics of physical systems governed by nonlinear partial differential equations. Initially, we give general procedure of the Cham technique for solving nonlinear partial differential equations that yields eight kinds of solutions. This technique is applied to the complex Ginzburg–Landau equation, incorporating five different types of nonlinearities: Kerr law, cubic–quintic law, polynomial nonlinearity, quadratic–cubic law, and parabolic-nonlocal law. With the aid of the proposed strategy, we can obtain a wide array of optical solitons, including bright, breather, kink, periodic, and cusp-shaped solitons, under specific parameter conditions.

Model free data assimilation with Takens embedding

In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of directly modeling the observation operator with noisy observation, we establish the state space model of the denoised observation. Through data assimilation techniques, the denoised observation information could be used to recover the original model state. Takens’ theorem shows that an embedding of the partial and denoised observation is diffeomorphic to the attractor. This gives a theoretical base for estimating the model state using the reconstruction map. To realize the idea, the procedure consists of offline stage and online stage. In the offline stage, we construct the surrogate dynamics using dynamic mode decomposition with noisy snapshots to learn the transition operator for the denoised observation. The filtering distribution of the denoised observation can be estimated using adaptive ensemble Kalman filter, without knowledge of the model error and observation noise covariances. Then the reconstruction map can be established using the posterior mean of the embedding and its corresponding state. In the online stage, the observation is filtered with the surrogate dynamics. Then the online state estimation can be performed utilizing the reconstruction map and the filtered observation. Furthermore, the idea can be generalized to the nonparametric framework with nonparametric time series prediction methods for chaotic problems. The numerical results show the proposed method can estimate the state distribution without the physical dynamical system.

PIDNODEs: Neural ordinary differential equations inspired by a proportional–integral–derivative controller

Neural Ordinary Differential Equations (NODEs) are a novel family of infinite-depth neural-net models through solving ODEs and their adjoint equations. In this paper, we present a strategy to enhance the training and inference of NODEs by integrating a Proportional–Integral–Derivative (PID) controller into the framework of Heavy Ball NODE, resulting in the proposed PIDNODEs and its generalized version, GPIDNODEs. By leveraging the advantages of control, PIDNODEs and GPIDNODEs can address the stiff ODE challenges by adjusting the parameters (i.e., Kp, Ki and Kd) in the PID module. The experiments confirm the superiority of PIDNODEs/GPIDNODEs over other NODE baselines on different computer vision and pattern recognition tasks, including image classification, point cloud separation and learning long-term dependencies from irregular time-series data for a physical dynamic system. These experiments demonstrate that the proposed models have higher accuracy and fewer function evaluations while alleviating the dilemma of exploding and vanishing gradients, particularly when learning long-term dependencies from a large amount of data.

An intelligent dynamic cyber physical system threat detection system for ensuring secured communication in 6G autonomous vehicle networks

Smart cities have developed advanced technology that improves people’s lives. A collaboration of smart cities with autonomous vehicles shows the development towards a more advanced future. Cyber-physical system (CPS) are used blend the cyber and physical world, combined with electronic and mechanical systems, Autonomous vehicles (AVs) provide an ideal model of CPS. The integration of 6G technology with Autonomous Vehicles (AVs) marks a significant advancement in Intelligent Transportation Systems (ITS), offering enhanced self-sufficiency, intelligence, and effectiveness. Autonomous vehicles rely on a complex network of sensors, cameras, and software to operate. A cyber-attack could interfere with these systems, leading to accidents, injuries, or fatalities. Autonomous vehicles are often connected to broader transportation networks and infrastructure. A successful cyber-attack could disrupt not only individual vehicles but also public transportation systems, causing widespread chaos and economic damage. Autonomous vehicles communicate with other vehicles (V2V) and infrastructure (V2I) for safe and efficient operation. If these communication channels are compromised, it could lead to collisions, traffic jams, or other dangerous situations. So we present a novel approach to mitigating these security risks by leveraging pre-trained Convolutional Neural Network (CNN) models for dynamic cyber-attack detection within the cyber-physical systems (CPS) framework of AVs. The proposed Intelligent Intrusion Detection System (IIDS) employs a combination of advanced learning techniques, including Data Fusion, One-Class Support Vector Machine, Random Forest, and k-Nearest Neighbor, to improve detection accuracy. The study demonstrates that the EfficientNet model achieves superior performance with an accuracy of up to 99.97%, highlighting its potential to significantly enhance the security of AV networks. This research contributes to the development of intelligent cyber-security models that align with 6G standards, ultimately supporting the safe and efficient integration of AVs into smart cities.

Neuromorphic overparameterisation and few-shot learning in multilayer physical neural networks

Physical neuromorphic computing, exploiting the complex dynamics of physical systems, has seen rapid advancements in sophistication and performance. Physical reservoir computing, a subset of neuromorphic computing, faces limitations due to its reliance on single systems. This constrains output dimensionality and dynamic range, limiting performance to a narrow range of tasks. Here, we engineer a suite of nanomagnetic array physical reservoirs and interconnect them in parallel and series to create a multilayer neural network architecture. The output of one reservoir is recorded, scaled and virtually fed as input to the next reservoir. This networked approach increases output dimensionality, internal dynamics and computational performance. We demonstrate that a physical neuromorphic system can achieve an overparameterised state, facilitating meta-learning on small training sets and yielding strong performance across a wide range of tasks. Our approach’s efficacy is further demonstrated through few-shot learning, where the system rapidly adapts to new tasks.

Bifurcation analysis and soliton structures of the truncated [formula omitted]-fractional Kuralay-II equation with two analytical techniques

The truncated M-fractional Kuralay (TMFK)-II equation is prevalent in the exploration of specific complex nonlinear wave phenomena. Such types of wave phenomena are more applicable in science and engineering. These equations could potentially provide insights into understanding the intricate dynamics of optical phenomena, encompassing solitons, nonlinear effects, and wave interactions. This study aims to uncover a diverse range of soliton solutions to the model, spanning trigonometric, hyperbolic, exponential, and rational expressions. These solutions are unveiled through the application of extended hyperbolic functions and improved F-expansion techniques, representing the primary objective of this research. The three-dimensional (3D) and two-dimensional (2D) combined charts are plotted for some of these solutions. The impact of the fractional parameters and time variations is also illustrated. Moreover, the models are converted into a planar dynamical system using a Galilean transformation, and the analysis of bifurcation is examined. This research underscores the versatility of the aforementioned techniques for exploring complex nonlinear phenomena across various engineering and scientific disciplines. Finally, the findings of this study hold significant implications for advancing our understanding and analysis of nonlinear wave dynamics in diverse physical systems.

Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems

Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering.

Research on the operation and quality control of small rock hole shotcrete robot

A small rock shotcrete robot is applied in the deep tunnel dynamic disaster physical simulation system in order to simulate the final operation process of the tunnel project. The robot’s spraying operation and control include many kind of factors. In this paper, the main parameters affecting the spraying operation are analyzed by establishing the spraying model and coating growth model. For matching reasonably the spraying parameters, the matching equation of spraying quality and spraying gun parameter model and spraying feed speed has been derived. Based on the matching equation, the spraying gun structure and robot control system are designed, and the spraying distance and spraying gun movement velocity including horizontal and vertical driving have been controlled better. On the basis of theoretical analysis, a small rock hole shotcrete robot prototype has been developed and the spraying experiments have been finished. The experimental results showed that the model and equation established can guided the spraying quality control. With the increase of the injection elevation angle, the length of the long and short axes of the elliptic coating becomes larger, and the average thickness of the coating center is between 2.23 and 2.34 mm, which meets the design index of the injection robot. The rock hole shotcrete robot meet the design requirements.

Applications of dynamical systems in physics

Dynamical systems are crucial for defining our comprehension of the physical world, offering a robust structure for examining and representing intricate occurrences. The exploration of dynamical systems in physics traces back to the initial developments of classical mechanics by Newton and Lagrange. Over time, this framework has developed and grown to encompass a broad array of physical phenomena, ranging from the movement of astronomical objects to the actions of subatomic particles. The close relationship between dynamical systems and physical principles has inspired the study and improvement of this mathematical field. This paper delves into the diverse applications of dynamical systems in physics, emphasizing the research background, methodology, main discoveries, and wider ramifications. This study tries to offer a thorough summary of the diverse impacts of dynamical systems on the area of physics by combining several research papers. By utilizing dynamical systems, researchers have gained a deeper understanding of the fundamental order that governs complex dynamics, paving the way for improved predictions, innovative technologies, and a deeper understanding of the underlying principles that govern the universe.

On qualitative analysis of a fractional hybrid Langevin differential equation with novel boundary conditions

A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional hybrid Langevin differential equation, including the ψ-Caputo fractional operator. Furthermore, some novel boundaries selected are considered to be a problem. We used the Schauder and Banach fixed-point theorems to prove the existence and uniqueness of solutions to the considered problem. Additionally, the Ulam-Hyer stability is evaluated. Finally, we present a representative example to verify the theoretical outcomes of our findings.

Turbulence and Rossby Wave Dynamics with Realizable Eddy Damped Markovian Anisotropic Closure

The theoretical basis for the Eddy Damped Markovian Anisotropic Closure (EDMAC) is formulated for two-dimensional anisotropic turbulence interacting with Rossby waves in the presence of advection by a large-scale mean flow. The EDMAC is as computationally efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure, but, in contrast, is realizable in the presence of transient waves. The EDMAC is arrived at through systematic simplification of a generalization of the non-Markovian Direct Interaction Approximation (DIA) closure that has its origin in renormalized perturbation theory. Markovian Anisotropic Closures (MACs) are obtained from the DIA by using three variants of the Fluctuation Dissipation Theorem (FDT) with the information in the time history integrals instead carried by Markovian differential equations for two relaxation functions. One of the MACs is simplified to the EDMAC with analytical relaxation functions and high numerical efficiency, like the EDQNM. Sufficient conditions for the EDMAC to be realizable in the presence of Rossby waves are determined. Examples of the numerical integration of the EDMAC compared with the EDQNM are presented for two-dimensional isotropic and anisotropic turbulence, at moderate Reynolds numbers, possibly interacting with Rossby waves and large-scale mean flow. The generalization of the EDMAC for the statistical dynamics of other physical systems to higher dimension and higher order nonlinearity is considered.

Non-Linear Dynamics of Simple Elastic Systems Undergoing Friction-Ruled Stick–Slip Motions

The stick–slip phenomenon is a jerking motion that can occur while two objects slide over each other with friction. There are several situations in which this phenomenon can be observed: between the slabs of the friction dampers used to mitigate vibrations in buildings, as well as between the components of the base isolation systems used for seismic protection. The systems of this kind are usually designed to work in a smooth and flawless manner, but under particular conditions undesired jerking motions may develop, yielding complex dynamic behavior even when only a few degrees of freedom are involved. A simplified approach to the problems of this kind leads to the mechanical model of a rigid block connected elastically to a rigid support and at the same time with friction to a second rigid support, both the supports having a prescribed motion. Despite the apparent simplicity of this model, it is very useful for studying important features of the non-linear dynamics of many physical systems. In this work, after a suitable formulation of the problem, the equations of motion are solved analytically in the sticking and sliding phases, and the influence of the main parameters of the system on its dynamics and limit cycles is investigated and discussed.

Development of Digital Twins for Urban Water Systems

Purpose: This paper provides an overview of the emerging concept of digital twins (DTs) for urban water systems (UWS), drawing from literature review, stakeholder interviews, and analysis of ongoing DT implementation at the utility company VCS Denmark (VCS). Methodology: Within the realm of UWS, DTs are situated across various levels, including component, unit process/operation, hydraulic structure, treatment plant, system, city, and societal levels. A UWS DT is described as a structured virtual representation of the physical system's elements and dynamics, organized in a star-structure format with interconnected features linked by data connections conforming to open data standards. Findings:This modular structure facilitates the breakdown of overall functionality into smaller units (features), fostering the emergence of microservices that communicate through data links, primarily facilitated by application programming interfaces (APIs). Integration with the physical system is achieved through simulation models and advanced analytics. Unique Contribution to theory, practice and policy: The paper suggests distinguishing between living and prototyping DTs, where "living" DTs entail coupling real-time observations from a dynamic physical twin with a simulation model through data links, while prototyping DTs represent system scenarios without direct real-time observation coupling, often used for design or planning purposes. Recognizing the existence of different types of DTs enables the identification of value creation across utility organizations and beyond. Analysis of the DT workflow at VCS underscores the importance of multifunctionality, upgradability, and adaptability in supporting potential value creation throughout the utility company. This study clarifies essential DT terminology for UWS and outlines steps for DT creation by leveraging digital ecosystems (DEs) and adhering to open data standards.

Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies.

In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is still relatively unexplored, especially in the context of excitatory and inhibitory interactions. In this work, we focus on the dynamics of the Kuramoto model on a circle with positive and negative connections paying attention to the existence of new attractors different from the synchronized state. Using analytical and computational methods, we find that even for identical oscillators, the introduction of inhibitory interactions modifies the structure of the attractors of the system. Our results extend the current understanding of synchronization in simple topologies and open new avenues for the study of collective dynamics in physical systems.

Correction to: Nonlinear system identification in coherence with nonlinearity measure for dynamic physical systems—case studies

Correction to: Nonlinear system identification in coherence with nonlinearity measure for dynamic physical systems—case studies

Causally‐Informed Deep Learning to Improve Climate Models and Projections

AbstractClimate models are essential to understand and project climate change, yet long‐standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid‐scale processes, particularly clouds and convection. Deep learning can learn these subgrid‐scale processes from computationally expensive storm‐resolving models while retaining many features at a fraction of computational cost. Yet, climate simulations with embedded neural network parameterizations are still challenging and highly depend on the deep learning solution. This is likely associated with spurious non‐physical correlations learned by the neural networks due to the complexity of the physical dynamical system. Here, we show that the combination of causality with deep learning helps removing spurious correlations and optimizing the neural network algorithm. To resolve this, we apply a causal discovery method to unveil causal drivers in the set of input predictors of atmospheric subgrid‐scale processes of a superparameterized climate model in which deep convection is explicitly resolved. The resulting causally‐informed neural networks are coupled to the climate model, hence, replacing the superparameterization and radiation scheme. We show that the climate simulations with causally‐informed neural network parameterizations retain many convection‐related properties and accurately generate the climate of the original high‐resolution climate model, while retaining similar generalization capabilities to unseen climates compared to the non‐causal approach. The combination of causal discovery and deep learning is a new and promising approach that leads to stable and more trustworthy climate simulations and paves the way toward more physically‐based causal deep learning approaches also in other scientific disciplines.

Mesh-based GNN surrogates for time-independent PDEs

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge—the edge augmented GNN and the multi-GNN. We show that both these networks perform significantly better than baseline methods, such as MeshGraphNets, when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings.

Nonlinear system identification in coherence with nonlinearity measure for dynamic physical systems—case studies

Nonlinear system identification in coherence with nonlinearity measure for dynamic physical systems—case studies

Coupled models for propagation of explosive shock waves in cylindrical and spherical geometries

The propagation of shock waves in different geometries is crucial in engineering and scientific applications. A comprehensive model is developed to elucidate the hydrodynamic growth and decay of shock waves in cylindrical and spherical geometries by using the strong shock wave assumption. This model takes into consideration the conservation equations governing mass, momentum, and energy, thereby allowing for an accurate description of the coupled behavior between the piston and shock wave propagation. In contrast to the localized analysis employed in previous self-similar methods, this model incorporates the finite sound wave velocity to introduce the concept of retarded pressure on the piston surface. Consequently, the proposed model offers a multitude of advantages by providing a complete set of dynamic information concerning the trajectories, velocities, and accelerations of both the piston and shock wave. Furthermore, an asymptotic analytical solution is derived to describe the decay of shock waves in cylindrical and spherical geometries. To validate the theoretical analysis and illustrate the propagation characteristics of shock waves in these specific geometries, thorough comparisons are conducted. These findings contribute to the advancement of our understanding of shock wave dynamics in various physical systems, particularly in the field of plasma physics.

Field-controlled dynamics of skyrmions and monopoles.

Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible for the onset of transitions between topologically distinct states and phases, such as in the case of transitions from helical and conical phase to A-phase comprising periodic arrays of skyrmions. By combining numerical modeling and optical characterizations, we describe how different geometrical configurations of skyrmions terminating at monopoles can be realized in liquid crystals and liquid crystal ferromagnets. We demonstrate how these complex structures can be effectively manipulated by external magnetic and electric fields. Furthermore, we discuss how our findings may hint at similar dynamics in other physical systems and their potential applications.