Stable Equilibrium State Research Articles

Correlation between the hierarchical structure evolution and Mullins effect of filled rubber under variable amplitude loading

Aiming to investigate the correlation between structure evolution and Mullins effect of filled silicone rubber, deuterated chain labeling and in situ small-angle neutron scattering (SANS) under variable amplitude loading have been conducted. The mechanical properties provide stress (σmax′) at the maximum strain (εmax), energy loss and recovery hysteresis (Es and Erh), etc. While the macrostructure such as radius of gyration Rg of aggregate covered with the bound rubber and the orientation can be obtained from SANS. All the parameters demonstrate consistently pattern in the two conditions of variable amplitude loading process. The evolution of crosslinking modulus Gc, the number of chain segment between entanglements ne/Te, amplification factors of filler X, etc. extracted from constitutive model further confirm such manners. With repeating cycles, the values reflecting mechanical properties such as σmax′ and Erh all exhibit a variation of less than 10%. Additionally, parameters related to microstructural evolution, such as X0 and Rg, also demonstrate a small variation of less than 10%. This implies that the system is in a state of stable equilibrium. With the εmax further increase, the amplitude of variation in orientation of bound rubber (th/tv-1) reaches 30%，ranging from 0.48 at S0.5C5 to 0.62 at S1.0C1, along with the variation of σmax′ around 75%, indicating the reversible deformation might transform into irreversible inelastic destruction and tend to an updated equilibrium.

Dynamics and application of a generalized SIQR epidemic model with vaccination and treatment

In this paper, we propose and investigate the SIQR epidemic model with a generalized incidence rate function, a general treatment function and vaccination term. We firstly consider the existence and uniqueness of the global nonnegative solution to the deterministic model. Further, we show the locally asymptotic stability of the disease-free equilibrium and endemic equilibrium of the deterministic model, and obtain the basic reproduction number R0. Then we study the existence and uniqueness of the global positive solution to the stochastic model with any positive initial value. Meanwhile, we obtain sufficient conditions for the extinction of the disease in the stochastic epidemic model, and find that the large noise can make the disease die out exponentially. Finally, we make an empirical analysis by the COVID-19 data of Russia and Serbia. By the performance comparison of different models, it shows that the model with vaccination and treatment we proposed is better for the real situation, which is also verified by different estimation methods. Especially, that shows the recovery rate of the infected increases by 0.042 and the death rate of the recovered is 1.525 times that of normal human in Russia. Through statistical analysis, the short-term trend of epidemic transmission is predicted: under the condition of unchanged prevention and control policies, it may reach a stable endemic equilibrium state in Russia and the epidemic will eventually extinct in Serbia.

Acoustic rotation of non-spherical micro-objects: Characterization of acoustophoresis and quantification of rotational stability

Acoustic radiation force and torque arising from wave scattering have the potential to perform the biocompatible, contact-free, and precise translation and rotation of micro-objects. Controllable rotation of objects mainly relies on the use of sophisticated transducer arrays, while it is limited by the spatial Rayleigh limitation and would be costly to miniaturize the array for manipulated objects on the micron scale. Here, we make use of the shape asymmetry of an object and achieve micro-object trap and rotation using a simple standing wavefield. The conformal transformation approach is employed to map an axisymmetric, non-spherical object into a sphere, allowing fast analysis for design or real-time computer-controlled manipulation. A low-cost, simple rotational tweezing system is built, which confirms the theoretical prediction that micro-particles are trapped in the pressure nodes and remotely rotated by the action of the actuator boundaries. The rotational dynamics are guided by two stabilization modes, and Lyapunov stability analysis reveals that at least one mode leads to a stable equilibrium state. We demonstrate the significance of our approach in stably and controllably rotating micron-scale objects. The robustness and versatility of the new handy design hold promise for clinical applications and microscopic research such as drug delivery and microsurgery.

On the global well-posedness for a multi-dimensional compressible Navier–Stokes–Poisson system

This article is dedicated to the study of the Cauchy problem for compressible Navier–Stokes–Poisson system in spatial dimensions two and higher. We prove the global well-posedness when the initial data are close to a stable equilibrium state in critical Lp framework.

Stabilization of the flat Poiseuille-type flow for viscoelastic polymeric liquid

This paper presents a numerical study for the problem of the one-dimensional flow of viscoelastic liquid polymers between two parallel plates. The equations of a rheologically modified Vinogradov–Pokrovskii (mVP) model is used for the formulation of the problem. It is shown that the problem could have multiple steady-state solutions. The evaluation of non-steady solutions was performed to see if the time-dependent solutions got eventually attracted by the steady ones. Also for the case of multiple steady solutions, it was checked which one attracts the non-steady solution if any. The evaluation of time-dependent solutions was used to estimate the stability of equilibrium states. It is revealed that stable steady-state regimes of the problem exist under certain conditions, and also there could be no more than one stable regime for any given set of parameters. The calculations were performed to estimate the values of Reynolds and Weissenberg numbers corresponding to either stable or unstable steady regimes. The result indicates that instability of the steady flow could possibly occur for arbitrary low Reynolds numbers under certain balance of viscous and elastic forces.

A coupled algebraic-delay differential system modeling tick-host interactive behavioural dynamics and multi-stability

We propose a coupled system of delay-algebraic equations to describe tick attaching and host grooming behaviors in the tick-host interface, and use the model to understand how this tick-host interaction impacts the tick population dynamics. We consider two critical state variables, the loads of feeding ticks on host and the engorged ticks on the ground for ticks in a particular development stage (nymphal stage) and show that the model as a coupled system of delay differential equation and an algebraic (integral) equation may have rich structures of equilibrium states, leading to multi-stability. We perform asymptotic analyses and use the implicit function theorem to characterize the stability of these equilibrium states, and show that bi-stability and quadri-stability occur naturally in several combinations of tick attaching and host grooming behaviours. In particular, we show that in the case when host grooming is triggered by the tick biting, the system will have three stable equilibrium states including the extinction state, and two unstable equilibrium states. In addition, the two nontrivial stable equilibrium states correspond to a low attachment rate and a large number of feeding ticks, and a high attachment rate and a small number of feeding ticks, respectively.

A novel spatial parallel multi-stable mechanism with eight stable states

A multi-stable flexible mechanism is a mechanical device that can switch to different stable equilibrium states under external power. Most existing multi-stable mechanisms are achieved by splicing bi-stable mechanisms. This paper proposes a novel Spatial Parallel Multi-stable Mechanism (SPMM) without bi-stable mechanisms connected, which even could achieve eight stable equilibrium states and meanwhile contain bi-stable mechanisms’ advantages such like simple structure and reliable abilities. To identify the equilibrium states, the paper develops a kinetostatic model using the Energy-Kinematics Differential Equations (EKDE) for the proposed SPMM. Based on the equilibrium states, the multi-stability topologies are drawn referring to direct groups, including the distribution of various equilibrium states and the switching paths between every two stable states. At last, the paper shows the experimental results of a 3D printed prototype and verify the eight-stability behaviors and the switching paths through unstable equilibrium states. A concept of the application in deformable cable protection shell using the SPMM is introduced.

On-demand ride-sourcing markets with cryptocurrency-based fare-reward scheme

Cryptocurrency-based fare-reward scheme has been emerging from on-demand ride-sourcing platforms. The reward scheme provides each passenger with some units of cryptocurrency as rewards for use of ride service. The passengers can redeem the rewards for various redemption options. The redemption options offer the passengers economic benefits to offset a portion of costs of using ride services. In this way, the economic benefits serve as incentives for the passengers to repeatedly use ride services, which leads to increase in passenger demand for the platforms. From a passenger perspective, the reward scheme has a distinctive feature in that economic benefits can fluctuate according to changes in price of cryptocurrency in the future. Therefore, the passengers perceive the benefits differently based on their own risk preference and expectation of future price changes. It creates a challenge for the platforms because the optimal decisions for ride services vary by the value that the passengers place for their cryptocurrency rewards. To tackle this challenge, this paper analyzes the impacts of the reward scheme on on-demand ride-sourcing markets. The analysis is done with a mathematical model where a ride-sourcing platform makes decisions for trip fare, vehicle fleet size and cryptocurrency reward size. The reward decision is available under the assumption that the platform secures as many units of cryptocurrency as it rewards to passengers at their equilibrium price level. The model defines passengers’ perceived value of cryptocurrency rewards in terms of risk aversion level and expectation of future price growth of cryptocurrency. Afterwards, we investigate equilibrium and optimal properties of monopoly, social-optimum and second-best optimum ride-sourcing markets. Our analysis gives several key insights on the markets. First, the markets always locate at normal regime where interactions between passenger demand and vehicle supply for ride services converges to a stable equilibrium state. Second, this study shows that a ride-sourcing platform would make a decision to reward if passengers expect larger economic benefits from future redemption of cryptocurrency rewards than their current value. Third, it is shown that the quality of ride services would get worse because average pick-up time for passengers and drivers gets longer with more passenger retention. Fourth, this paper finds that the markets have more room to improve profit or social welfare as passengers expect larger speculative gains from reward redemption.

Rate-dependent evolution of wrinkling films due to growth on semi-infinite planar viscoelastic substrates

A mechanistic understanding of morphogenesis in biology, the fabrication of advanced meta surfaces with specific functionalities and structures with enhanced energy dissipation often have in common that the combined effects of energy dissipation due to viscoelasticity and a loss of stability govern both their mechanical response and their final forms. In this paper we show that the interplay between viscoelasticity and multistability crucially influences the evolution of deformations in viscoelastic structures undergoing large deformations. The influence is studied on a prototypical system of a uniaxially growing film on a semi-infinite planar viscoelastic substrate, where it is shown that during the evolution of deformation the choice of multiple developing modes is greatly affected by this interplay. For the analysis of the underlying mechanics of the mode competition in the post-buckling regime, when the system undergoes large deformations, a 3D general finite-strain visco-hyperelastic theory is built. It includes kinematic and material nonlinearities in the film and in the substrate. For the case of ramp-loading time functions the phase space of the solutions is characterized and the evolution of a deformation pattern is analyzed. We find that the interaction between multistability and viscoelasticity greatly increases the evolution time of the system and that the growth rate and viscoelastic stress-relaxation rate influence the choice of the final equilibrium deformation state of the structure. This shows that viscoelastic structures can evolve into (meta)stable equilibrium states that are unattainable using purely elastic structures. The nonlinear problem is solved numerically with the use of the finite-element method. In parallel, we develop analytical solutions for a simplified problem that is based on Föppl–von Karman plate kinematics to describe the mechanics of the film and substrate that is modeled as a 2D linear-viscoelastic continuum. A remarkably good match between the analytical and the numerical results was obtained.

Mechanism and Control of Water–Rock Coupling-Induced Disaster when Mining below the Unconsolidated Confined Aquifer

Theoretical analysis and numerical simulation were conducted to study the disaster-causing mechanism of structural instability of the overlying strata induced by water–rock coupling and effectively prevent and control the powered support jammed accident during mining below the unconsolidated confined aquifer. The influencing factors on the stability of the overlying strata structure were analyzed, and the numerical simulation method of unconsolidated confined aquifer was designed. The disaster-causing mechanism and the evolution process of the stress–displacement–crack field of the overlying strata induced by water–rock coupling were discovered. Meanwhile, the prevention measures for the structural instability of the overlying strata were proposed and verified in some engineering practice. Results show that the stability of the overlying strata structure reduces with the increase in hydraulic pressure, the breaking interval of the main roof, and the decrease in the overlying strata strength and waterproof coal pillar height. The overlying strata structure keeps a stable equilibrium state before the fracture planes through a whole waterproof coal–rock pillar. When the hydraulic pressure is small or the bedrock surface is a thick topsoil layer, the sliding block is in a state of limit equilibrium for the decrease of pressure on the sliding block while the fracture planes through a whole waterproof coal–rock pillar because of the action of unloading during an overlying strata movement. When the hydraulic pressure is high, the pressure on the sliding block remains constant at about hydraulic pressure, and the intact shear fall of the sliding block occurs as a result of the hydraulic pressure of the confined aquifer and the weight of the sliding block, which may result in a powered support jammed accident. However, this type of accident can be prevented by drainage for decreasing hydraulic pressure, presplitting blasting of the hard main roof, overlying strata grouting reinforcement, and increasing the height of the waterproof coal–rock pillar.

Cooperative game-based multi-objective optimization of cargo transportation with floating partial space elevator

This paper develops a dual-phase control strategy based on the piecewise cooperative game method to balance the multiple competing objectives for cargo transportation by a partial space elevator in terms of orbital state stability and cargo transport efficiency and ensure final state stability. The cargo transportation is performed in the libration-free mode to facilitate the control implementation, where all libration motions are kept at zero. The new control strategy is split into phases I and II. Phase I focuses on cargo transportation and covers most cargo transfer distances. Multiple competing control objectives in this phase are balanced by the newly proposed piecewise cooperative game method. Once the remaining distance meets the preset threshold, the transportation enters phase II, which focuses on bringing the state of the partial space elevator to a stable equilibrium state. A shrinking horizon model predictive control method is used to ensure the state converges to the equilibrium point by the end of transportation. The simulation results reveal that the newly proposed dual-phase control scheme effectively balances multiple competing control objectives in the cargo transfer period. Moreover, by introducing phase II, the system can achieve a stable equilibrium state by the end of the transfer period.

Light-Controlled Rotational Speed of an Acoustically Levitating Photomobile Polymer Film.

In this work, we study the light-induced changes of the rotational speed of a thin photomobile film using a single-axis acoustic levitator operating at 40 kHz. In our experiments, a 50 μm thick photomobile polymer film (PMP) is placed in one of the nodes of a stationary acoustic field. Under the action of the field, the film remains suspended in air. By externally perturbing this stable equilibrium condition, the film begins to rotate with its natural frequency. The rotations are detected in real time by monitoring the light of a low power He-Ne laser impinging on and reflected by the film itself. During the rotational motion, an external laser source is used to illuminate the PMP film; as a consequence, the film bends and the rotational speed changes by about 20 Hz. This kind of contactless long-distance interaction is an ideal platform for the development and study of many electro-optics devices in microgravity and low-friction conditions. In particular, we believe that this technology could find applications in research fields such as 3D dynamic displays and aerospace applications.

Impact of pollution on sardine, sardinella, and mackerel fishery: a bioeconomic approach

This paper studies a bioeconomic model of three species of small pelagic marine species in Moroccan coastal areas: Sardine, Sardinella and shark. The model combines competition and predation. Two areas are proposed, one is polluted and the other is not. The model combines a biological part describing the evolution of the biomass of stocks subjected to fishing mortality and an economic part explaining the mortality rate. We study the existence and stability of equilibrium states through eigenvalue analysis and the Routh-Hirwitz criterion, then introduce economic approaches to determine the effort needed to maximize the fishermen’s income. Numerical simulations are performed. The objective of this paper is to study the impact of pollution on the existence, evolution of biomass and predation, fishing effort, catches, and profits.

A Random Memory Length Adaptive Algorithm for Vertex Cover Problem

The vertex cover (VC) problem has been studied for past few years, and some centralized and distributed algorithms have been proposed. In this paper, we propose the so-called random memory length adaptive (RMLA) algorithm for the VC problem in networks. Any initial state can reach the stable pure strict Nash equilibrium state through finite iterations by the RMLA algorithm. We find that by setting the minimum edge-keeping probability reasonably, the convergence rapidity and accuracy can be improved simultaneously. Our algorithm also removes the requirement for consistent node memory length. Through theoretical analysis and intensive numerical simulations, we verify the convergence and effectiveness of the RMLA algorithm.

Innovation Development of an Enterprise: Modeling Dynamics

At the present stage of economic development, the leading role in ensuring the competitiveness of both an singular enterprise and the country as a whole, as well as in creating conditions for the transition to sustainable development, is played by the successful implementation of the latest scientific developments in production processes, comprehensive support for the strategy of innovative development. The development and implementation of innovations is a complex dynamic process that requires the use of special research methods. Such a method is system dynamics, which makes it possible to take into account the nonlinearity of the impact of innovation on the state of the economy. The paper considers the methodology for building a model for managing innovation processes, taking into account the self-organization of the logistic type. The main danger that can accompany the evolution of innovation processes is the emergence of unacceptable dynamic modes, so one of the tasks of the study was to determine the conditions capable of ensuring the stability of equilibrium states of a complex dynamic system according to the proposed models. The object of research is a complex dynamic system, between the elements of which there is both positive and negative feedback. To build a model of the dynamics of innovation processes, the mathematical apparatus of the theory of differential equations was applied, which made it possible to consider the development of the innovation process in continuous time. With the help of the instrumentarium of nonlinear dynamics, a study of the stability of diffusion of innovations depending on the parameters of the control influence was carried out. The conditions for the transition of the system to a critical state, which may be accompanied by the occurrence of bifurcations and chaos, have been determined. Particular attention was paid to determining the structural stability of the regulated innovation process in the case when both equilibrium positions are close in terms of parameter values. It is expedient to apply the proposed model to solve the problem of innovation management both at the State level and at the level of an individual industry or an individual enterprise. The obtained theoretical conclusions were confirmed through the use of simulation modeling.

Dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings

The subject of this work is the study of local dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings. From a discrete model describing the dynamics of a great number of coupled oscillators, a transition has been made to a nonlinear integro-differential equation, continuously depending on time and space variable. A class of full-coupled systems has been considered. The main assumption is that the amount of delay in the couplings is large enough. This assumption opens the way to the use of special asymptotic methods of study. The parameters under which the critical case is realized in the problem of the equilibrium state stability have been distinguished. It is shown that they have infinite dimension. The analogues of normal forms — nonlinear boundary value problems of Ginzburg–Landau type have been constructed. In some cases, these boundary value problems contain integral components too. Their nonlocal dynamics describes the behavior of all solutions of the original equations in the balance state neighbourhood. Methods. As applied to the considered problems, methods of constructing quasinormal forms on central manifolds are developed. An algorithm for constructing the asymptotics of solutions based on the use of quasinormal forms for determining slowly varying amplitudes has been created. Results. Quasinormal forms that determine the dynamics of the original boundary value problem have been constructed. The dominant terms of asymptotic approximations for solutions of the considered chains have been obtained. On the basis of the given statements, a number of interesting dynamical effects have been revealed. For example, an infinite alternation of direct and reverse bifurcations when the delay coefficient increases. Their distinguishing feature is that they have two or three spatial variables.

How to Promote Quality and Equity of Early Childhood Education for Sustainable Development in Undeveloped Rural Areas of China: An Evolutionary Game Study

To promote the sustainable development of early childhood education (ECE) in undeveloped rural areas of China, it is vital to guarantee high-quality equity for all children from disadvantaged backgrounds. Focusing on analyzing the efficacy of the Chinese governments’ policy support to promote quality and equity, the study constructs a tripartite evolutionary game model of ECE providers in undeveloped rural areas, local governments, and central government, and correlates the governments’ financial investment with the regulation and supervision in ECE as strategy combination via a reward-punishment mechanism. Through the evolution process of “change-adjustment-convergence” of behavioral decisions, each party seeks optimization to achieve the ideal stable equilibrium state. The numerical simulation is used to verify the dynamic evolutionary process. The simulation results presented the governments’ subsidies and reward, regulation, and supervision have a substantive effect on the improvement of quality and equity. Consequently, the governments should strengthen the regulation and supervision of rural ECE, formulate a more reasonable reward and punishment mechanism, and adjust and optimize the policies and measures to improve the efficiency of educational funding. This study can provide reference value for the optimization of relevant policies and the practical operation of new policy-making.

Asymptotic analysis of SIR epidemic model with nonlocal diffusion and generalized nonlinear incidence functional

We aim in this research to determine the global stability of equilibrium states for an SIR epidemic model with nonlocal diffusion and nonlinear incidence function in a heterogeneous environment. For achieving this result, we consider that the model parameters are Lipschitz continuous functions. At the infection free‐equilibrium, the eigenvalue problem has a principal simple eigenvalue corresponding to strictly positive eigenfunction which is expressed as . By a Lyapunov function approach, we show the global stability of drug‐free equilibrium for . For , and using persistence theory for dynamical systems, we show that the epidemic will persist and the unique endemic equilibrium state is globally stable by constructing a proper Lyapunov function.

A basic community dynamics experiment: Disentangling deterministic and stochastic processes in structuring ecological communities.

Community dynamics are governed by two opposed processes: species sorting, which produces deterministic dynamics leading to an equilibrium state, and ecological drift, which produces stochastic dynamics. Despite a great deal of theoretical and empirical work aiming to demonstrate the predominance of one or the other of these processes, the importance of drift in structuring communities and maintaining species diversity remains contested. Here, we present the results of a basic community dynamics experiment using floating aquatic plants, designed to measure the relative contributions of species sorting and ecological drift to community change over about a dozen generations. We found that species sorting became overwhelmingly dominant as the experiment progressed, and directed communities toward a stable equilibrium state maintained by negative frequency-dependent selection. The dynamics of any particular species depended on how far its initial frequency was from its equilibrium frequency, however, and consequently the balance of sorting and drift varied among species.

Faster network disruption from layered oscillatory dynamics.

Nonlinear complex network-coupled systems typically have multiple stable equilibrium states. Following perturbations or due to ambient noise, the system is pushed away from its initial equilibrium, and, depending on the direction and the amplitude of the excursion, it might undergo a transition to another equilibrium. It was recently demonstrated [M. Tyloo, J. Phys. Complex. 3 03LT01 (2022)] that layered complex networks may exhibit amplified fluctuations. Here, I investigate how noise with system-specific correlations impacts the first escape time of nonlinearly coupled oscillators. Interestingly, I show that, not only the strong amplification of the fluctuations is a threat to the good functioning of the network but also the spatial and temporal correlations of the noise along the lowest-lying eigenmodes of the Laplacian matrix. I analyze first escape times on synthetic networks and compare noise originating from layered dynamics to uncorrelated noise.