Equilibrium State Research Articles

NONLINEAR DYNAMICS METHODS APPLICATIONS TO PRODUCT LIFECYCLE MANAGEMENT

The research being carried out is aimed at applying nonlinear dynamics methods in product life cycle management to improve communication between processes and achieve environmental sustainability. The purpose of the article is to create a nonlinear mathematical model for analysing product lifecycle management. Chaotic nonlinear dynamical processes of product lifecycle are deterministic but have the property that even small uncertainties in initial conditions lead to exponentially growing errors in the management that limit long-term forecasts. The emergence of chaotic behaviour in processes of product lifecycle was explored, focusing on fluctuations. The study employed methods such as systems analysis, correlation analysis, nonlinear dynamics, and the Surrogate model of chaotic Lorenz waterwheel. It was identified that sharp technological innovations as the primary drivers of short-term fluctuations impacting fixed efficiency and effectiveness of product life cycle process development. The resulting nonlinear dynamic model allowed for flexible operation, transitioning between equilibrium, periodic, and chaotic states based on coefficient values for asset growth rates and time constants reflecting product life cycle process dynamics. The research results are valuable for companies seeking to reduce their environmental impact and implement circular economy principles.

Analyzing a Dynamical System with Harmonic Mean Incidence Rate Using Volterra–Lyapunov Matrices and Fractal-Fractional Operators

This paper investigates the dynamics of the SIR infectious disease model, with a specific emphasis on utilizing a harmonic mean-type incidence rate. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. A sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V-L) matrices, is developed to examine the overall trajectory of the model globally. In addition to that, we describe the transmission of infectious disease through a mathematical model using fractal-fractional differential operators. We prove the existence and uniqueness of solutions in the SIR model framework with a harmonic mean-type incidence rate by using the Banach contraction approach. Functional analysis is used together with the Ulam–Hyers (UH) stability approach to perform stability analysis. We simulate the numerical results by using a computational scheme with the help of MATLAB. This study advances our knowledge of the dynamics of epidemic dissemination and facilitates the development of disease prevention and mitigation tactics.

A comprehensive analysis of COVID-19 nonlinear mathematical model by incorporating the environment and social distancing

This research conducts a detailed analysis of a nonlinear mathematical model representing COVID-19, incorporating both environmental factors and social distancing measures. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. The study develops a sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V–L) matrices method. To understand the dynamic behavior of COVID-19, numerical simulations are essential. For this purpose, the study employs a robust numerical technique known as the non-standard finite difference (NSFD) method, introduced by Mickens. Various results are visually presented through graphical representations across different parameter values to illustrate the impact of environmental factors and social distancing measures.

The impact of gaseous degradation on the gas–particle partitioning of methylated polycyclic aromatic hydrocarbons

Abstract. The partitioning of semi-volatile organic compounds (SVOCs) between gas and particle phases plays a crucial role in their long-range transport and health risk assessment. However, the accurate prediction of the gas–particle (G–P) partitioning quotient (KP′) remains a challenge, especially for the light-molecular-weight (LMW) SVOCs due to their upward deviation from equilibrium state. In this study, the phenomenon with the influence of gaseous degradation on G–P partitioning was observed. Based on the diurnal study of concentrations and KP′ values for methylated polycyclic aromatic hydrocarbons (Me-PAHs), it was found that the KP′ values of methylated naphthalenes (Me-Naps; one type of LMW SVOC) during the daytime were higher than during the nighttime, and the regression lines of log KP′ versus log KOA (octanol–air partitioning coefficient) for daytime and nighttime were non-overlapping, which were different from other Me-PAHs. Compared with other diurnal influencing factors, the higher gaseous degradation of Me-Naps in the daytime than in the nighttime should partially explain their special diurnal variation in KP′, which provided a new explanation for the non-equilibrium behavior of KP′ for LMW SVOCs. Moreover, the influence of gaseous degradation on the deviation of KP′ from equilibrium state was deeply studied based on the steady-state G–P partitioning model considering particulate proportion in emission (ϕ0). The increasing times of KP′ influenced by the gaseous degradation deviated from equilibrium state can be calculated by 1 + 13.2ϕ0 × kdeg (kdeg, gaseous degradation rate). The increase in KP′ along with the increase in kdeg proved that higher gaseous degradation in the daytime could increase the KP′ value. Furthermore, an amplification in KP′ ranging from 1.11 to 5.58 times (90 % confidence interval: 1.01 to 14.4) under different ϕ0 values (0 to 1) in the temperature range of −50 to 50 °C was estimated by the Monte Carlo analysis. In summary, it can be concluded that the influence of gaseous degradation should also be considered in the G–P partitioning models of SVOCs, especially for the LMW SVOCs, which provided new insights into the related fields.

Analysis on the synergy between markets of electricity, carbon, and tradable green certificates in China

China has integrated tradable green certificates and carbon markets with its electricity sector to promote renewable energy and reduce carbon emissions. However, the impact mechanism of decision-making behaviors of involved entities in these integrated markets on the market equilibrium is still unclear, hence limiting the further development of renewable energy industries and carbon reduction progress to some extent. Therefore, conducting in-depth research to inform policy makers about the impacts of entities' decision-making behaviors on market equilibrium within the context of integrated multiple markets is crucial. This study aims to analyze the characteristics of entities' decision-making behaviors and equilibrium states within the collaborative dynamics of carbon, electricity, and green certificate markets. Specifically, an optimal decision-making model for entities given the multi-market coupling was developed by employing mathematical programming methods to analyze market equilibriums across various market combinations and policy parameters. The conclusions underscore equilibrium price shifts and decision-making characteristics among entities across multiple markets. The result shows that the carbon market could increase power prices and decrease green certificate prices. To ensure sustainable energy development, policymakers should consider the decision-making behavior of entities under multi-market coupling, which can promote the low-carbon transformation of the Chinese energy industry.

Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir

Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. This is particularly true for quantum mechanical systems. We demonstrate here how, through a mechanism of repeated scattering, an approach to equilibrium of this type actually occurs in a specific quantum system, one that can be viewed as a natural quantum analog of several previously studied classical models. In particular, we consider an optical mode passing through a reservoir composed of a large number of sequentially-encountered modes of the same frequency, each of which it interacts with through a beam splitter. We then analyze the dependence of the asymptotic state of this mode on the assumed stationary common initial state σ of the reservoir modes and on the transmittance τ=cos⁡λ of the beam splitters. These results allow us to establish that at small λ such a mode will, starting from an arbitrary initial system state ρ, approach a state of thermal equilibrium even when the reservoir modes are not themselves initially thermalized. We show in addition that, when the initial states are pure, the asymptotic state of the optical mode is maximally entangled with the reservoir and exhibits less nonclassicality than the state of the reservoir modes.

Enhanced entanglement in multi-bath spin-boson models

The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.

Demonstration of Controlled Skyrmion Injection Across a Thickness Step.

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

Surface snow bromide and nitrate at Eureka, Canada, in early spring and implications for polar boundary layer chemistry

Abstract. This study explores the role of snowpack in polar boundary layer chemistry, especially as a direct source of reactive bromine (BrOx = BrO + Br) and nitrogen (NOx = NO + NO2) in the Arctic springtime. Surface snow samples were collected daily from a Canadian high Arctic location at Eureka, Nunavut (80° N, 86° W) from the end of February to the end of March in 2018 and 2019. The snow was sampled at several sites representing distinct environments: sea ice, inland close to sea level, and a hilltop ∼ 600 m above sea level (a.s.l.). At the inland sites, surface snow salinity has a double-peak distribution with the first and lowest peak at 0.001–0.002 practical salinity unit (psu), which corresponds to the precipitation effect, and the second peak at 0.01–0.04 psu, which is likely related to the salt accumulation effect (due to loss of water vapour by sublimation). Snow salinity on sea ice has a triple-peak distribution; its first and second peaks overlap with the inland peaks, and the third peak at 0.2–0.4 psu is likely due to the sea water effect (a result of upward migration of brine). At all sites, snow sodium and chloride concentrations increase by almost 10-fold from the top 0.2 to ∼ 1.5 cm. Surface snow bromide at sea level is significantly enriched, indicating a net sink of atmospheric bromine. Moreover, surface snow bromide at sea level has an increasing trend over the measurement period, with mean slopes of 0.024 µM d−1 in the 0–0.2 cm layer and 0.016 µM d−1 in the 0.2–0.5 cm layer. Surface snow nitrate at sea level also shows a significant increasing trend, with mean slopes of 0.27, 0.20, and 0.07 µM d−1 in the top 0.2, 0.2–0.5, and 0.5–1.5 cm layers, respectively. Using these trends, an integrated net deposition flux of bromide of (1.01 ± 0.48) × 107 molec.cm-2s-1 and an integrated net deposition flux of nitrate of (2.6 ± 0.37) × 108 molec.cm-2s-1 were derived. In addition, the surface snow nitrate and bromide at inland sites were found to be significantly correlated (R = 0.48–0.76) with the [NO3-]/[Br-] ratio of 4–7 indicating a possible acceleration effect of reactive bromine in atmospheric NOx-to-nitrate conversion. This is the first time such an effect has been seen in snow chemistry data obtained with a sampling frequency as short as 1 d. BrO partial column (0–4 km) data measured by MAX-DOAS show a decreasing trend in early spring, which generally agrees with the derived surface snow bromide deposition flux indicating that bromine in Eureka atmosphere and surface snow did not reach a photochemical equilibrium state. Through mass balance analysis, we conclude that the average release flux of reactive bromine from snow over the campaign period must be smaller than the derived bromide deposition flux of ∼ 1 × 107 molec.cm-2s-1. Note that the net mean fluxes observed do not completely rule out larger bidirectional fluxes over shorter timescales.

Exploring cyclic dominance in rock-paper-scissor strategies within the Optional Prisoner's Dilemma: A quantitative analysis with environmental feedback

This research investigation delves into the concept of cyclic dominance and its interplay with environmental feedback within the framework of the Optional Prisoner's Dilemma (OPD) game. A quantitative model has been meticulously constructed to encompass both the OPD and Rock-Paper-Scissors (RPS) games, wherein the outcomes are contingent upon environmental feedback. The intricate relationship between player populations and their surrounding environment is elucidated through the utilization of replicator dynamics. The empirical findings of this study shed light on the existence of distinct equilibria contingent upon the prevailing environmental circumstances. Under scenarios characterized by resource depletion, an equilibrium state emerges wherein only solitary individuals (referred to as "loners") persist. Conversely, under conditions of resource replenishment, an equilibrium is established where various strategic approaches coexist in equal proportions, akin to the dynamics of the Rock-Paper-Scissors game. Notably, cyclic dominance manifests itself during periods characterized by intermediate environmental conditions. Several pivotal factors have been identified as determinants of these dynamic phenomena, including the rate of environmental replenishment, the strength of the dilemma presented, the payoff for loners, and the reward for a draw. It has been empirically demonstrated that the presence of extreme values in the replenishment rate, irrespective of whether exceptionally high or exceptionally low, serves as an impediment to the emergence of cyclic dominance. This model underscores the substantial influence of environmental feedback on social dilemmas, particularly in the context of the OPD game, ultimately leading to the emergence of competitive cyclic dominance games reminiscent of the Rock-Paper-Scissors game. In doing so, it elucidates the intricate interplay between evolutionary game incentives and the dynamics of the surrounding environment.

Thermal response of nematicons in a parabolic potential

Abstract The thermal response of nematicons in a parabolic potential has been
numerically studied. Single-peak nematicons exist only in the absence of thermal
response coefficients. Because focusing reorientational nonlinearity is dominant in
this case. In the presence of thermal response, the competition between focusing
reorientational and defocusing thermal nonlinearities leads to the transformation of
single-peak to double-peak nematicons. In this domain, the defocusing thermal
nonlinearity is greater than the focusing reorientational nonlinearity, resulting in
double-peak nematicons. The energy landscape experienced by the light beam within
the medium is modified by the competing nonlinearities. The presence of both
focusing reorientational and defocusing thermal nonlinearities creates multiple maxima
in the energy landscape, allowing for the stabilization of double-peak nematicons as
equilibrium states. When a parabolic potential is present, periodic oscillations can
be obtained in nematicon. For small values of thermal response coefficients, doublepeak
nematicons having periodic oscillations are obtained. The thermal response
coefficients have significant impacts on the wavelength of the oscillations of doublepeak
nematicon. The wavelength has been found to increase with increasing thermal
response coefficients. Large values of the thermal response coefficients result in a
double-peak nematicon with no oscillations. The linear stability analysis shows that
single-peak nematicons and double-peak nematicons having periodic oscillations are
stable, while double-peak nematicon with a non-oscillatory nature is unstable.

Refining Combustion Dynamics: Dissolved Hydrogen in Diesel Fuel within Turbulent-Flow Environments

This article presents the possibility of improving combustion using the effect of releasing hydrogen from a solution with nucleation of gas bubbles. This concept consists in dissolving hydrogen in diesel fuel until the equilibrium state of the solution is reached. At a later stage, the phenomenon is reversed, and this gas is released from the solution during its injection into the combustion chamber with a strong swirl. A characteristic feature of the solution is that when lowering the pressure (opening the atomizers), there is a decrease in the equilibrium thermodynamic potential, which results in the excess, dissolved hydrogen being released spontaneously, and this process is of a volumetric nature. This article is a continuation of the work carried out at Poznan University of Technology on the development of this concept. This article presents the results of tests for the impact of hydrogen dissolved in diesel fuel on the combustion process within a turbulent-flow environment. The tests were conducted in the combustion chamber of an engine equipped with a toroidal combustion chamber and direct injection. During the tests, the following factors were measured: the main indicators of motor operation, emission of hydrocarbons, carbon monoxide, nitrogen oxides, and particulate matters.

Self-Organization and Phase Transitions in Driven Cellular Automata.

The Game of Life (GoL) cellular automaton is modified to inject order during execution of the state transition algorithm by making selected stable structures permanently active while interacting with normal active sites to create novel structures. A survey of the modified automaton's phenomenology and an analysis of its dynamics are presented in the context of the physics of the self-organization of matter by viewing the GoL as an artificial chemistry. These new structures become seeds for additional phases of structure building, analogous to nature's gravitational and thermodynamic churning of the geosphere that created material structures in phases, beginning the transition from geochemistry to prebiotic chemistry and laying foundational substrates for life-enabling organizational processes in an emerging biosphere. Evidence of selective self-assembly during phase transitions is reported where several GoL still life structures, configured as permanently active seeds evolving with random collections of active sites, resulted in geometrically identical structures as the GoL reached an equilibrium state of static density.

Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics.

What is the Role of Gravity, Turbulence and Magnetic Fields in High-mass Star Formation Clouds?

To explore the potential role of gravity, turbulence and magnetic fields in high-mass star formation in molecular clouds, this study revisits the velocity dispersion–size (σ–L) and density–size (ρ–L) scalings and the associated turbulent energy spectrum using an extensive data sample. The sample includes various hierarchical density structures in high-mass star formation clouds, across scales of 0.01–100 pc. We observe σ ∝ L 0.26 and ρ ∝ L −1.54 scalings, converging toward a virial equilibrium state. A nearly flat virial parameter–mass (α vir−M) distribution is seen across all density scales, with α vir values centered around unity, suggesting a global equilibrium maintained by the interplay between gravity and turbulence across multiple scales. Our turbulent energy spectrum (E(k)) analysis, based on the σ–L and ρ–L scalings, yields a characteristic E(k) ∝ k −1.52. These findings indicate the potential significance of gravity, turbulence, and possibly magnetic fields in regulating dynamics of molecular clouds and high-mass star formation therein.

Hydrostatic Equation of State of bcc Bi by Directly Solving the Partition Function

Body−centered cubic bismuth (Bi) is considered to be an enticing pressure marker, and, therefore, it is highly desirable to command its accurate equation of state (EOS). However, signifi­cant discrepancies are noted among the previous experimental EOSs. In the present work, an EOS of up to 300 GPa is theoretically obtained by solving the partition function via a direct integral ap­proach (DIA). The calculated results nearly reproduce the hydrostatic experimental measurements below 75 GPa, and the deviations from the measurements gradually become larger with increasing pressure. Based on the ensemble theory of equilibrium state, the DIA works with high precision particularly in high−pressure conditions, so the hydrostatic EOS presented in this work is expected to be a reliable pressure standard.

Practical Design of a Breed-and-Burn Lead-Cooled Fast Reactor with Rotational Fuel Shuffling Strategy

The purpose of this study is to demonstrate a practical core design for a lead-cooled, nitride fueled, rotational fuel shuffling breed-and-burn (RFBB) fast reactor. The core design is based on the Westinghouse Lead Fast Reactor (WH-LFR) and uses natural uranium nitride fuel with a sodium bond encased in oxide dispersion-strengthened steel cladding. Simulations confirmed the potential of the reactor to maintain criticality at the equilibrium state, with a reactivity swing of less than 200 pcm at every cycle interval and an average discharge burnup of 235 MWd/kg heavy metals (HM) for a 1050 effective full-power day refueling interval. Power profiles were maintained stable at the equilibrium state, while the cladding of the discharged fuel incurred over 650 displacements per atom over its entire residency in the core. From a nonproliferation perspective, the plutonium vector for the discharge fuel aligns with reactor-grade fuel standards, with over a 70% concentration of 239Pu and over 22% 240Pu, reducing the risk of weaponization. The adopted control rod system has been shown to offer sufficient negative reactivity of over 19 $ to bring the reactor into a subcritical state. Challenges such as the susceptibility of neutron balance to material thickness and neutron leakage have been addressed, emphasizing the necessity for meticulous design improvements. A steady-state thermohydraulic analysis confirmed the heat removal capacity from the hottest channel, ensuring operational safety. This study confirmed the feasibility of the RFBB strategy for a lead-cooled nitride-fueled fast reactor and sets a precedent for future research in enhancing fuel utilization and safety in nuclear reactors.

Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities

In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary control for the specified hyperbolic system is given. A difference scheme is constructed for the numerical solution of the considered initial boundary value problem. The definition of the exponential stability of the numerical solution in ℓ2-norm with respect to a discrete perturbation of the equilibrium state of the initial boundary value difference problem is given. A discrete Lyapunov function for a numerical solution is constructed, and a theorem on the exponential stability of a stationary solution of the initial boundary value difference problem in ℓ2-norm with respect to a discrete perturbation is proved.

A Novel Calculate Model of Shear Deformation and Relative Displacement of Pile–Soil Interface in Warm Frozen Soil Foundation

In permafrost regions with warm frozen soil, the pile foundation is commonly used, but most currently available models for the WFS foundation pile–soil system are either highly empirical or overcomplicated, without a simplified theoretical manner in engineering. This study derives a novel and simplified calculated model of the WFS pile–soil system. The model is formulated in terms of the shear deformation theory and load transfer method based on the rigorous deformation mechanism of the WFS foundation soil around the pile. Considering the different depth soil features and the equilibrium state of the pile–soil system, dividing warm frozen soil foundation into three regions (TPPR, ER, and BPPR) to calculate the Dp and Ds can simply obtain the total displacement of pile under different loads. The results demonstrate that the present theoretical model can well predict the WFS foundation load–displacement response of the pile. The present model provides a simple, practical, and effective approach for the estimation of the load–displacement behavior of piles installed in the WFS foundation.

Development of a neural network model for peeling-ballooning stability analysis in the KSTAR tokamak pedestals

Abstract The neural network model, MISHKA-NN is developed to mitigate the computational burden associated with the linear ideal MHD stability analysis of the pedestal based on the peeling-ballooning model. By utilizing both 1D plasma profiles (current density, pressure gradient, and safety factor) and 0D parameters (plasma geometry, total current, and toroidal mode number), the model predicts linear growth rate of edge-localized ideal MHD instability in a given equilibrium state. By enabling the prediction of each instability within a second, the model reduces the time required for plotting a pedestal peeling-ballooning stability diagram ($j-\alpha$ diagram) from approximately 100 CPU hours to a few CPU minutes. Notably, even with the utilization of parametric pressure and current profiles and plasma boundary shapes for the training dataset, the model shows a satisfactory level of performance in benchmarking the $j-\alpha$ diagram for the reconstructed equilibrium from a KSTAR tokamak experiment. We anticipate the model to serve as a versatile alternative to 2D linear MHD stability codes, alleviating numerical costs.