Multidimensional Systems Research Articles

Wavelet-based collocation methods for solving multi-dimensional integro-differential systems

This paper presents a comprehensive investigation of wavelet-based collocation methods for solving multi-dimensional integro-differential systems. The research addresses the challenging problem of finding numerical solutions to integro-differential equations (IDEs) that are essential in various scientific and engineering applications. We propose novel numerical approximations for infinitely dimensional problems, including fractional Cattaneo-Rayleigh waves and nonlinear diffusion problems defined on unbounded domains. The study introduces a unified computational strategy that directly applies to IDEs without discretization, particularly focusing on the integer and fractional-order Cattaneo-Rayleigh model of thermoelasticity in one-dimensional zonal regions. Through numerical experiments, we demonstrate that our wavelet collocation approach achieves high efficiency and superior accuracy compared to traditional methods. The results show particularly strong performance in handling systems with differential physical singularities, functional physical singularities, and vector-valued physical singularities. Our approach provides a valuable toolbox for addressing complex modeling challenges in biology, mechanical signal processing, and digital communications where partial integro-differential equations naturally arise.

Analytical generalized thermal resistance model for conductive heat transfer in pebble beds based on heat flux weighted temperature difference

A novel model for inter-particle contact thermal resistance based on analytical solutions is proposed. By applying the concept of heat flux weighted temperature difference in thermal resistance modeling for the first time, this model offers greater physical significance than traditional thermal resistance models. It effectively describes the dissipation in the heat transfer process and the influence of particle radius on thermal resistance, making it a generalized thermal resistance model suitable for multi-dimensional systems. The impact of applying different levels of uniform heat flux boundary conditions on thermal resistance is analyzed from the perspective of energy dissipation, revealing that a more uniform heat flux input results in lower thermal resistance. The effects of contact radius and particle size on the dimensionless generalized thermal resistance of inter-particle contact were studied, showing that the dimensionless resistance increases with larger particle contact radius and smaller particle size. Using the thermal discrete element method, the thermal resistance model with uniform heat flux density boundary conditions was applied to calculate the effective thermal conductivity of the pebble bed. Considering the distribution of contact radius, differences in effective thermal conductivity at various heights of the pebble bed due to different contact radii were examined and compared with the traditional fixed-coefficient contact resistance model. It was found that the difference between the two models decreases as the contact radius decreases. Finally, multiple sets of fixed contact radii were established under three different particle sizes, revealing that as the contact radius increases, the deviation between the new generalized resistance model and the traditional fixed-coefficient model rises from 8.18 % to 14.64 % for different particle radii.

Chaotic vibration control of an axially moving string of multidimensional nonlinear dynamic system with an improved FSMC

A new control approach based on fuzzy sliding mode control (FSMC) is proposed to regulate the chaotic vibration of an axial string. Hamilton’s principle is used to formulate the nonlinear equation of motion of the axial translation string, and the von Kármán equations are used to analyse the geometric nonlinearity. The governing equations are nondimensionalized as partial differential equations and transformed into a nonlinear 3-dimensional system via the third-order Galerkin approach. An active control technique based on the FSMC approach is suggested for the derived dynamic system. By using a recurrent neural network model, we can accurately predict and effectively apply a control strategy to suppress chaotic movements. The necessity of the suggested active control method in the regulation of the nonlinear axial translation string system is proven using different chaotic vibrations. The results show that the study of the chaotic vibrations of axially translating strings requires nonlinear multidimensional dynamic systems of axially moving strings; the validity of the proposed control strategy in controlling the chaotic vibration of axially moving strings in a multidimensional form is demonstrated.

State-of-the-art nonstationary hypersurface damage assessment approach for energy harvesters

Since EH (Energy Harvesters) constitute nowadays a vital part of renewable energy engineering, experimental research is required in addition to numerical modeling, serving reliable structural design and ensuring prolonged device service time. The performance of GPEH (GalloPing EH) has been examined in this case study, utilizing comprehensive laboratory wind tunnel tests, carried out under realistic windspeed conditions. Novel structural multivariate risks assessment methodology, presented here, being feasible for nonstationary nonlinear GPEH dynamic systems, that had been either physically measured over a representative period, providing jointly quasi-ergodic time-series, or directly numerically MCS (Monte Carlo Simulated). Based on laboratory-measured GPEH dynamics, the presented analysis demonstrates that the proposed multivariate hypersurface methodology offers robust predictions of the structural failure/damage risks. Furthermore, when dealing with raw measured timeseries, representing the high-dimensional dynamic system, existing risk assessment techniques struggle to handle nonlinear inter-correlations between GPEH critical components. This case study's main objective has been to validate and benchmark the novel multimodal risk assessment methodology, which utilizes multivariate nonstationary lab-recorded time histories to extract relevant design information from the underlying GPEH dynamics.The proposed state-of-the-art nonstationary hypersurface reliability approach being of a generic nature, offering additional capacity for damage/failure risks prognostics for a wide range of nonlinear multidimensional nonstationary systems. Forecasted damage and failure risks have been supplied with confidence bands, demonstrating the experimental setup's robustness, as well as the useful design features of the presented nonstationary hypersurface risks assessment methodology. It should be noted that the presented reliability methodology being mathematically exact, and it does not rely on simplifying assumptions.

Leveraging recommendations using a multiplex graph database

PurposeBy applying targeted graph algorithms, the method used by the authors enables effective prediction of user interactions and thus fulfils the complex requirements of modern recommender systems. This study sets a new benchmark for multidimensional recommendation strategies and offers a path towards more advanced and user-centric models.Design/methodology/approachTo improve multidimensional data recommendation systems, multiplex graph structures are useful to capture various types of user interactions. This paper presents a novel framework that uses a graph database to compute and manipulate multiplex graphs. The approach enables flexible dimension management and increases expressive power through a specialised algebra designed for multiplex graph manipulation.FindingsThe authors compare the multiplex graph approach with traditional matrix methods, in particular random walk with restart, and show that the method not only provides deeper insights into user preferences by integrating scores from different layers of the multiplex graph, but also outperforming matrix-based approaches in most configurations. The results highlight the potential of multiplex graphs for developing sophisticated and customised recommender systems that significantly improve both performance and explainability.Originality/valueThe study provides a formal specification of a multiplex graph construction based on interaction and content-based information; and the study also developed an algebra dedicated to multiplex graphs, enabling robust and precise graph manipulations necessary for effective recommendation queries. The authors implement these algebraic operations within the Neo4j graph database system with a thorough analysis and experimentation with three different data sets, benchmarked against traditional matrix-based methods.

Construction and Validation of Academic Support Scale in Middle School (ASSMS)

Research on social support in China has been relatively comprehensive as psychological development cannot be separated from the social environment. Family, teachers, and friends are the main sources of social support for middle school students. If we can fully utilize the academic support provided by families, teachers, and classmates in daily life, improve students’ personal efficacy, stimulate their learning motivation and desire, and provide corresponding emotional, resource, behavioral, and willingness support for middle school students, it will help them better enhance their learning adaptability, increase their investment in learning, and then improve their learning consciousness, ultimately promoting the enhancement of academic achievement and the development of their abilities. Therefore, based on the existing scales of social support and academic support, this study determined the academic support scale for middle school students, exploring the source of academic support from four dimensions: willingness support, resource support, emotional support, and behavioral support. Based on a literature review and questionnaire, a formal scale was formed to measure the academic support of middle school students. In total, 762 students from two middle schools in Shijiazhuang and Hengshui were selected as subjects for data analysis. Exploratory factor analysis showed that the scale was composed of four factors: willingness support, resource support, emotional support, and behavioral support, with a cumulative contribution rate of 54.15%. The factor loadings of the items ranged from 0.423 to 0.783. The indicators obtained by confirmatory factor analysis were χ2/df of 2.98, RMSEA of 0.072, GFI of 0.841, IFI of 0.902, TLI of 0.891, and CFI of 0.901. The Cronbach’s α coefficient was 0.955, the Spearman–Brown coefficient was 0.939, and the correlation coefficients between each dimension and the total scale were 0.892–0.945. The results show that the reliability and validity of the scale are within the acceptable range, in line with the standards of measurement, and can be used as a tool to measure the academic support of middle school students. This measurement can be used to evaluate the multidimensional academic support systems in middle schools and inform the development of targeted interventions to promote student success and well-being.

Boundary null controllability of some multi-dimensional linear parabolic systems by the moment method

Boundary null controllability of some multi-dimensional linear parabolic systems by the moment method

Robust theory of thermal activation in magnetic systems with Gilbert damping

Magnetic systems can exhibit thermally activated transitions whose timescales are often described by an Arrhenius law. However, robust predictions of such timescales are only available for certain cases. Inspired by the harmonic theory of Langer, we derive a general activation rate for multidimensional spin systems. Assuming local thermal equilibrium in the initial minimum and deriving an expression for the flow of probability density along the unstable dynamical mode at the saddle point, we obtain the expression for the activation rate that is a function of the Gilbert damping parameter, α. We find that this expression remains valid for the physically relevant regime of α≪1. When the activation is characterized by a coherent reorientation of all spins, we gain insight into the prefactor of the Arrhenius law by writing it in terms of spin wave frequencies and, for the case of a finite spin chain, obtain an expression that depends exponentially on the square of the system size indicating a break-down of the Meyer-Neldel rule. Published by the American Physical Society 2024

A Hybrid Concept Analysis of Frailty Among Older Adults Living in the Community.

To analyse the concept of frailty through a literature review and in-depth interviews. A hybrid model of concept analysis. The theoretical phase identified 43 articles for reviewing the definition and measurement of frailty. Seven frail older adults were invited in the fieldwork phase for in-depth interviews. In the final analysis phase, results from the fieldwork and theoretical phases were integrated to obtain a final definition of frailty. Attributes of frailty were heterogeneous, involving dynamic/bidirectional, multidimensional and multiple systems. The antecedents of the concept were exposure to various stimuli and challenges in responding to these stimuli. Consequences included losing autonomy and adverse health outcomes. Four themes of frailty were identified based on the fieldwork data: 'accumulation of functional decline', 'powerlessness of coping with', 'vicissitudes of lived experience' and 'loss of autonomy and positivity'. The final definition of frailty was 'a dynamic and fluctuating process of powerlessness to manage biopsychosocial and environmental stimuli, involving functional decline and vicissitudes of life, which results in losing autonomy and positivity or adverse health outcomes'. Characterising the definition of frailty is essential for nurses to address the lived experiences of older adults when providing person-centred care and for developing interventions that meet the needs of frail older adults. Since some discrepancies existed in the definition of frailty from individual perception of older adults, combined in-depth interviews with a theoretical literature review were used to provide comprehensive insight. This concept analysis provides guidelines of training for nurses and opportunities to improving quality of life for community dwelling older adults. N/A. No Patient or Public Contribution.

Fokker–Planck equation and Feynman–Kac formula for multidimensional stochastic dynamical systems with Lévy noises and time-dependent coefficients

The aim of this paper is to establish a version of the Feynman–Kac formula for the time-dependent multidimensional nonlocal Fokker–Planck equation corresponding to a class of time-dependent stochastic differential equations driven by multiplicative symmetric (or asymmetric) α-stable Lévy noise. First the forward nonlocal Fokker–Planck equation is derived by the adjoint operator method, overcoming the challenges posed by time-dependent multidimensional nonlinear symmetric α-stable Lévy noise. Subsequently, the Feynman–Kac formula for the forward multidimensional time-dependent nonlocal Fokker–Planck equation is established by applying techniques for the backward nonlocal Fokker–Planck equations, which is associated with the backward stochastic differential equation driven by the multiplicative symmetric α-stable Lévy noise. Notably, in the case of asymmetric α-stable Lévy noise case, the presence of the characteristic function in the nonlocal operator adds complexity to the analysis. Using the Feynman–Kac formula, it is demonstrated that the solution of the forward nonlocal Fokker–Planck equation can be readily simulated through Monte Carlo approximation, especially in scenarios involving long-time simulation settings with large steps. These concepts are illustrated with intriguing examples, and the dynamic evolution of the probability density function corresponding to the stochastic SIS model and the stochastic model for the MeKS network (reflecting the interactions among the MecA complex, ComK and ComS) are investigated over an extended period.

Caribbean Society and Organisation: Change and Transformation

Established and strongly embedded forms of inclusion and exclusion, tension and dynamic between the formal and the informal exists within Caribbean organisations. A study of organisational change was undertaken in two Jamaican organisations of 22 participants each, and questions raised about this transformational problematic of organisation/development and change. The study, set against the backdrop of structural-psycho-socio-cultural dynamics, investigated the way that employees cognitively appraised organisational change. A comparative multi-dimensional systems approach was employed and also an examination and discussion of different levels of organisational embeddedness, with intersecting levels involving interstitial margins. The findings confirmed the importance of focused leadership, communication and high levels of disruption, uncertainty and expectancy associated with prolonged change efforts and the role of status and power. The study is the first of its kind, however, further research is needed to better understand the interactions of structural and psycho-socio-cultural demands on organisational change in diverse organisational settings.

Complex systems for controlling thermal modes of radio-electronic equipment

The system of providing thermal conditions of radio-electronic equipment, which is a necessary subsystem of such modern information systems as on-board mobile objects with high requirements to reliability, dynamics and controllability, is analyzed. A solid-state method of cooling energy generation based on the Peltier effect is highlighted, which has such advantages as the possibility of creating a temperature below ambient, small dimensions, mass and increased reliability compared to similar coolers of other physical principles. It is shown that in distributed systems with heat-loaded elements the function of transporting heat flows is necessary, and the most promising for the solved problems is realized on flexible heat pipes, which agree with thermoelectric coolers in terms of reliability, mass and dimensional characteristics. The method of reducing the mass and dimensional characteristics of systems for providing thermal modes with impulse heat generation, typical for tracking systems or on-board systems, is considered. It is noted that the heat of phase transition of melting substances allows to form thermal accumulators, which, when coordinated with the dynamic characteristics of thermal processes of the system, allows to significantly reduce the mass and dimensional characteristics of the system for providing thermal modes. The use of thermal accumulators in systems with pulse-periodic influence allows to increase also reliability indicators due to filtration of high-frequency thermal emissions in heat-loaded elements. The expediency of the system approach to the design of the thermoelectric system for ensuring thermal modes of electronic equipment with heat pipes and thermal accumulators by synthesizing a multidimensional regulator type “Multiple Input - Multiple Output” (MIMO) is substantiated. It is substantiated that to satisfy the basic principles of multidimensional systems of fragility and robustness it is necessary to satisfy the condition of creation of a qualitative model of the thermoelectric system of provision of thermal modes of heat-loaded electronic equipment.

An improved RRT behavioral planning method for robots based on PTM algorithm

For multi-dimensional high-order nonlinear systems with unstable path quality in parameter and extension terms, we developed a new fast search random tree strategy. First, we established a high-order Lipschitz vector field dynamic system to adapt to high-order systems of multi-degree-of-freedom robots, with the complex obstacle function being one of its key components. Secondly, we designed a classification gap filtering network layer (Classification LSTM) to screen training data models and ensure the global stability of data in path design. Additionally, the visual sensors deployed in the unit area effectively implement the path marking backtracking strategy and dead zone path simplification. Finally, three examples are provided to verify the effectiveness of this design method.

Limit hypersurface state-of-the-art damage assessment approach for a galloping energy harvester, accounting for memory effects

Energy harvesters (i.e., EH) constituting nowadays an essential part of renewable energy engineering; hence, apart from numerical modeling, experimental studies are necessary, constituting reliable input for durable design and structural safety assessments. In the current study, galloping EH’s performance was analyzed, utilizing extensive laboratory wind-tunnel tests, conducted under realistic windspeed conditions. The novel structural multivariate risks assessment methodology, presented in the current study is particularly feasible for multi-dimensional nonlinear EH dynamic systems, that have been either directly Monte Carlo (i.e., MC) numerically simulated or physically measured over a representative temporal lapse, providing piecewise ergodic time series. As shown in this analysis, the suggested multivariate methodology accurately enables accurate predictions of the EH dynamic system’s failure/hazard or damage risks, based on laboratory-measured EH system’s dynamics. Furthermore, nonlinear inter-correlations between various systems’ critical components are not always easily handled by classic risk assessment techniques, when dealing with a high-dimensional system’s raw time series. The primary goal of this study was validation and benchmarking the novel risk assessment methodology, which can extract pertinent information, contained within the EH system’s dynamics, based on lab-recorded time histories. In conclusion, the novel hypersurface methodology presented in this study is generic, providing additional capability to accurately, yet efficiently predict damage/failure risks for a variety of nonlinear EH multidimensional systems. Relatively narrow confidence bands have been reported for the forecasted damage and failure levels, indicating both the robustness of the experimental setup, as well as practical design virtues of the advocated Gaidai hypersurface risks assessment methodology. Note that the presented methodology being mathematically exact does not rely on pre-assumptions and yet it is of general purpose.

Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure

In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the admissible Hamiltonian operators. We present in detail the examples of two-dimensional, two-components systems of hydrodynamic type and of a real reduction of the 3-waves system.

Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems

We are concerned with the Prandtl-Meyer reflection configurations of unsteady global solutions for supersonic flow impinging upon a symmetric solid wedge. Prandtl (1936) first employed the shock polar analysis to show that there are two possible steady configurations: the steady weak shock solution and the steady strong shock solution, when a steady supersonic flow impinges upon the solid wedge – the half-angle of which is less than a critical angle (i.e., the detachment angle), and then conjectured that the steady weak shock solution is physically admissible since it is the one observed experimentally. The fundamental issue of whether one or both of the steady weak and strong shocks are physically admissible has been vigorously debated over the past eight decades and has not yet been settled in a definitive manner. On the other hand, the Prandtl-Meyer reflection configurations are core configurations in the structure of global entropy solutions of the two-dimensional Riemann problem, while the Riemann solutions themselves are local building blocks and determine local structures, global attractors, and large-time asymptotic states of general entropy solutions of multidimensional hyperbolic systems of conservation laws. In this sense, we have to understand the reflection configurations in order to understand fully the global entropy solutions of two-dimensional hyperbolic systems of conservation laws, including the admissibility issue for the entropy solutions. In this monograph, we address this longstanding open issue and present our analysis to establish the stability theorem for the steady weak shock solutions as the long-time asymptotics of the Prandtl-Meyer reflection configurations for unsteady potential flow for all the physical parameters up to the detachment angle. To achieve these, we first reformulate the problem as a free boundary problem involving transonic shocks and then obtain appropriate monotonicity properties and uniform a priori estimates for admissible solutions, which allow us to employ the Leray-Schauder degree argument to complete the theory for all the physical parameters up to the detachment angle.

Ocean windspeeds forecast by Gaidai multivariate risk assessment method, utilizing deconvolution scheme

The current work presents spatiotemporal analysis of areal windspeeds, using state-of-the-art Gaidai multivariate hazards evaluation approach. Environmental dynamic systems being challenging to forecast using existing reliability methods due to their high dimensionality and intricate nonlinear cross-correlations between different environmental system essential dimensions or components. Developing novel multivariate reliability methods for dynamic environmental systems may assist contemporary research on the global climate change effects. Multivariate Gaidai risks evaluation approach is especially well-suited for multi-dimensional structural and environmental dynamic systems, that have been monitored physically or numerically simulated across a representative time-lapse. The current study made use of raw in-situ windspeed data, collected by NOAA (i.e., National Oceanic and Atmospheric Administration) buoys near the Hawaiian Islands in the North Pacific. Resilient island communities/infrastructure can be designed, using advocated multivariate risk/hazard assessment methodology, particularly those that are close to the ocean and hence subject to extreme weather.As was demonstrated in this study, even given limited underlying dataset, it is feasible to conservatively estimate environmental system’s hazard risks. Novel non-parametric deconvolution extrapolation scheme has been utilized to accurately assess hazard risks.

Image encryption algorithm based on DNA mutation and a novel four-dimensional hyperchaos

Abstract Aiming at the problem that insufficient complexity of ordinary multi-dimensional chaotic systems and the cumbersome design of encryption algorithms without excellent encryption effects. This paper constructs a four-dimensional hyperchaotic system with high Lyapunov exponent and complex dynamic behavior. We designed an encryption algorithm based on point mutation, mutation diffusion, and folding mutation in DNA mutations. During the encryption process, we perform point mutation transformation on the entire base sequence, then spread the mutations one by one starting from the second base of the sequence, and finally flip every four base sequences according to folding mutations. The images encrypted by this algorithm have a uniform grayscale histogram, high information entropy, and high key sensitivity. It can resist exhaustive attacks, noise attacks, cropping attacks, and differential attacks, and have a fast encryption speed.

Empowering a qudit-based quantum processor by traversing the dual bosonic ladder

High-dimensional quantum information processing has emerged as a promising avenue to transcend hardware limitations and advance the frontiers of quantum technologies. Harnessing the untapped potential of the so-called qudits necessitates the development of quantum protocols beyond the established qubit methodologies. Here, we present a robust, hardware-efficient, and scalable approach for operating multidimensional solid-state systems using Raman-assisted two-photon interactions. We then utilize them to construct extensible multi-qubit operations, realize highly entangled multidimensional states including atomic squeezed states and Schrödinger cat states, and implement programmable entanglement distribution along a qudit array. Our work illuminates the quantum electrodynamics of strongly driven multi-qudit systems and provides the experimental foundation for the future development of high-dimensional quantum applications such as quantum sensing and fault-tolerant quantum computing.

A worldwide review of formal national street classification plans enhanced via an analytical hierarchy process: Street classification as a tool for more sustainable cities

For cities to utilise their maximum liveability potential, their transport infrastructure and overall service provision need to function seamlessly. To this end, urban street eco-systems should be characterised, organised and utilised effectively. But is this happening on a mass scale across the globe? Are our urban street classification schemes forward-thinking and ready to respond to the emerging sustainability and resilience challenges cities face nowadays? This paper aims to answer these questions by examining and decoding the prevailing “formal street classification scheme model” through conducting a detailed worldwide review of formal national street classification plans. Out of 196 countries investigated, 128 official street classification plans were identified, analysed and evaluated. We also used an Analytical Hierarchy Process (AHP) with 20 experts coming from different fields (i.e., academics, policymakers, practitioners) to enhance our results and contribute to developing an index evaluating urban street classification under the prism of sustainability. The outcomes of our work signify that conventional pro-automobile approaches still prevail, thus shaping car-centric conditions, which undermine the role of sustainable modes and reduce the ability of cities to innovate and succeed. It is demonstrated that the road to achieve sustainability and completeness in urban transport systems, considering these car-led plans, is still uphill. Based on that, multi-dimensional classification systems prioritising public and active transport, while appreciating street's urban aspect should be promoted in the future.