Stable Equilibrium State Research Articles

Conditions for Stable Equilibrium of the Upright Human Body in the Absense and Presence of External Influence

The proposal article is the union of the two previous scientific works [1,2]. The given paper studies conditions of the equilibrium stability of a cylinder - shaped homogeneous body. Thus, conditions of the equilibrium stability of different proportion upright standing men were studied. A new method allowing determination of a man’s common centre of gravity was developed. An optimal bending forward angle at which the degree of the equilibrium stability of an upright standing man reaches its maximum value was determined. Hence, the appropriate conclusions were drawn. External forces are introduced herein, which may disturb the stable equilibrium and cause the body to tumble. The paper also introduces the concept of the coefficient of the stable equilibrium and proposes a formula for its calculation. Finally, a formula is set up to obtain the maximum value of external forces under which the body still maintains the state of equilibrium.

Evolutionary Game Analysis of Electric Vehicle Distribution Entities with Shared Charging Facilities

This study investigates the evolutionary game dynamics among electric vehicle distribution entities in the context of shared charging facilities, addressing the critical issue of inadequate charging resources. To understand the behavior of different stakeholders under government incentive policies, we develop an evolutionary game model involving a government department and two logistics enterprises (A and B). Through stability analysis, we explore equilibrium conditions of evolutionarily stable strategies (ESSs) for the tripartite evolutionary game. To ensure the robustness of our findings, we conduct a MATLAB simulation analysis to validate the analytical results. Our findings highlight that government subsidies, the costs incurred by logistics enterprises to share charging facilities, and the additional distribution income derived from this sharing are critical in determining whether the evolutionary game can achieve a stable equilibrium state. This research enables logistics companies to optimize the use of charging resources, lower operating costs, and enhance delivery efficiency. Additionally, government subsidy policies play a crucial role in encouraging logistics enterprises to engage in charging facility sharing, thereby fostering the sustainable development of the entire logistics industry. Based on these insights, the paper offers practical recommendations to further promote the sharing of charging facilities in electric vehicle distribution.

Assembly of phyllosphere bacterial community with PsnWRKY70 in poplar

Plant microbiome plays an important role in growth and development, biotic and abiotic stresses, and genotype is one of the key factors in shaping the microbiome. In this study, the effect of PsnWRKY70 on the synthetic bacterial community of poplar was investigated. To explore the assembly mechanism of poplar phyllosphere bacteria. we used 39 strains of bacteria isolated from the phyllosphere of poplar to construct a synthetic bacterial community. The leaves of aseptic poplar tissue culture seedlings were inoculated with synthetic bacterial community, and the bacterial communities of poplar leaves inoculated with synthetic bacterial community for 0 d, 5 d, 10 d and 15d were sequenced for 16 s. Bacterial community composition, PCoA, and Lefse analyses were performed. The results showed that the bacterial community in the phyllosphere of poplar tended to be in a stable equilibrium state after inoculation with the synthetic bacterial community. The results of β diversity analysis showed that there were significant differences in the bacterial community structure of OE, RE and WT leaves at 5d and 10 d after inoculation with Syncom. It is mainly composed of Methylobacteriaceae, Enterbacteriaceae, Agrobacterium, Rhizobium, Pseudoxanthomonas and Stenotrophomonas. The results of differential bacterial analysis showed that Paracoccus, Arthrobacter and Rhodococcus had higher relative abundance and stability in OE line. PsnWRKY70 gene plays an important role in recruiting Paracoccus, Arthrobacter and Rhodococcus strains in poplar leaves.

Советский социализм: о природе и уроках проекта

Abstract. This article explores the prerequisites, content, and outcomes of the Soviet project. The term refers to the predominance of arbitrary organization of social reality over its naturally-historical self-determination. Unlike the utopian denial of existing social being, the project is viewed as a technological compensation for the mediating disruptions and interruptions in evolutionary trends. The Soviet period of national history is examined as the largest known endeavor to create a new society, vividly illustrating the inherent internal dialectics that underscore the stability and viability of a constructed consciousness of existence. However, this dual nature imposes a strict limit on such a construction: the act of historical arbitrariness is incapable of transcending the nearest state of stable equilibrium within the social system, where the objective laws of social development reclaim their unlimited authority. Moreover, the earlier inability to impose self-restraint leads arbitrariness to its own negation.

Synchronization analysis of a four-motor excitation with torsion spring coupling vibrating system

In oil drilling processes, vibrating screen is a crucial solid control equipment for separating harmful solid-phase particles. However, the conventional utilization of either dual-motor or triple-motor is inadequate demanding the excitation force of large vibrating equipment. Moreover, self-synchronization in zero phase is difficult to achieve in multiple motors system. To avoid cancellation of the excitation force caused by the phase inconsistency of multiple motors, the adoption of a four-motor excitation with torsion spring coupling system is proposed this work. Initially, the mathematical model of the vibrating system is formulated through the Lagrange's equation. Subsequently, the steady-state solution is determined using Laplace transform. Then the conditions and characteristics in stable equilibrium state are elucidated employing the small parameter averaging method. Ultimately, the reliability and applicability of the theoretical results are substantiated through numerical simulations. The findings reveal that with the increase of the torsion spring stiffness, the phase difference between the motors connected by torsion springs (MCTSs) is exponentially decreased, and desired zero-phase synchronization in engineering is eventually achieved. Furthermore, the present study uncovers two distinct synchronization mechanisms in the torsion spring coupling system: mechanical controlled synchronization between MCTSs is inevitably achieved, while the self-synchronization between motors unconnected by torsion springs (MUTSs) is limited by the synchronization conditions. The study provides valuable insights for designing mechanical controlled synchronization and self-synchronization vibrating machines.

Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity

In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.

Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules

This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of 3n exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are 3n synchronization manifolds, wherein n is the number of neurons. Additionally, an estimation for the settling time required for drive–response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.

All-magnonic repeater based on bistability

Bistability, a universal phenomenon found in diverse fields such as biology, chemistry, and physics, describes a scenario in which a system has two stable equilibrium states and resets to one of the two states. The ability to switch between these two states is the basis for a wide range of applications, particularly in memory and logic operations. Here, we present a universal approach to achieve bistable switching in magnonics, the field processing data using spin waves. A pronounced bistable window is observed in a 1 μm wide magnonic conduit under an external rf drive. The system is characterized by two magnonic stable states defined as low and high spin-wave amplitude states. The switching between these two states is realized by another propagating spin wave sent into the rf driven region. This magnonic bistable switching is used to design a magnonic repeater, which receives the original decayed and distorted spin wave and regenerates a new spin wave with amplified amplitude and normalized phase. Our magnonic repeater can be installed at the inputs of each magnonic logic gate to overcome the spin-wave amplitude degradation and phase distortion during previous propagation and achieve integrated magnonic circuits or magnonic neuromorphic networks.

Convective Instability Driven by Diffusiophoresis of Colloids in Binary Liquid Mixtures.

In a binary fluid mixture, the concentration gradient of a heavier molecular solute leads to a diffusive flux of solvent and solute to achieve thermodynamic equilibrium. If the solute concentration decreases with height, the system is always in a condition of stable mechanical equilibrium against gravity. We show experimentally that this mechanical equilibrium becomes unstable in case colloidal particles are dispersed uniformly within the mixture and that the resulting colloidal suspension undergoes a transient convective instability with the onset of convection patterns. By means of a numerical analysis, we clarify the microscopic mechanism from which the observed destabilization process originates. The solute concentration gradient drives an upward diffusiophoretic migration of colloids, in turn causing the development of a mechanically unstable layer within the sample, where the density of the suspension increases with height. Convective motions arise to minimize this localized rise in gravitational potential energy.

Stability Of Equilibrium States For A Stochastically Perturbed Pielou’s Equation [

Stability Of Equilibrium States For A Stochastically Perturbed Pielou’s Equation [

Singular Phenomenon Analysis of Wind-Driven Circulation System Based on Galerkin Low-Order Model

Ocean circulation plays an important role in the formation and occurrence of extreme climate events. The study shows that the periodic variation of ocean circulation under strong wind stress is closely related to climate oscillation. Ocean circulation is a nonlinear dynamic system, which shows complex nonlinear characteristics, so the essence behind ocean circulation has not been clearly explained. Therefore, the response and evolution of the circulation system to wind stress are studied based on the bifurcation and catastrophe theories in nonlinear dynamics. First, the quasi-geostrophic gyre equation and the normalized gravity model are introduced and developed to study ocean circulation driven by wind stress, and solved using the Galerkin method. Then, the bifurcation and catastrophe behaviors of the system governed by the low-order ocean circulation model during the change in wind stress intensity and the coexistence of multiple equilibria in the circulation system are studied in detail. The results show that saddle and unstable nodes appear in the system after a cusp catastrophe. With the change in model parameters, the unstable node becomes the unstable focus, and then the subcritical Hopf bifurcation occurs. The system forms a bistable interval when the system undergoes a catastrophe twice, and the system shows hysteresis. In addition, multiple equilibrium states are coexisting in the circulating system, and the unstable equilibrium state always changes into a stable equilibrium state through vortex movement. Therefore, there is a route for the system to induce short-term climate oscillation, that is, in the multi-stable equilibrium state of the system, the vortex oscillates after being subject to small disturbances, and then triggers climate oscillation.

Dynamics of chains of a large number of fully coupled oscillators, as well as oscillators with one-way and two-way delay couplings

This articles considers chains consisting of identical nonlinear equations of second order with couplings in linear elements. It is assumed that there is a large delay in the coupling elements. Moreover, we assume that the chain possesses a large number of elements. Therefore, instead of the original system with many elements, we can study a second order nonlinear integro-differential equation with periodic boundary conditions. The main study is focused on the local dynamics of chains with one-sided, two-sided couplings, as well as fully coupled chains. Also, we study the stability of equilibrium states and identify the critical cases. The condition of a sufficiently large delay helps to determine the parameters for the implementation of critical cases explicitly. Our methodology is based on the infinite-dimensional normalisation method proposed by the author, namely the method of quasinormal forms. We construct quasinormal forms for the chains under consideration that determine the asymptotics of the leading terms of the asymptotic expansions of the solutions to the original system.

Stability of equilibrium states for a stochastic difference equation of exponential form

It is well know that many process and problems in different fields of sciences and engineering can be modelled by linear and nonlinear difference equations. Particularly, in case of systems biology, ecology, biochemistry, genetics and physiology dynamics, many population models are governed by exponential difference equations, and lot of papers were published in this matter. The goal of this work is to study a nonlinear second order difference equation of exponential form: Xn+1 = bXn + cXne−σXn−1, n ≥ 0 where the parameters b, c have arbitrary values, σ > 0 and the initial values, X0, X−1 are arbitrary positive numbers. Our equation has an equilibrium points and is exposed to additive stochastic perturbations that are assumed a sequence of independent random variables with zero mean, unit variance and these perturbations are proportional to the deviation of the system state Xn from equilibrium points, and the result is stochastic difference equation. We cannot find the solutions of nonlinear stochastic difference equations of exponential form in all cases. So, one can study the behavior of solutions by asymptotic stability of equilibrium points. Additionally, with the general method of Lyapunov functional constructions for stochastic difference equations with discrete time, we provide the necessary and sufficient conditions for the asymptotic mean square stability of the two equilibrium points (zero and positive) within the linear approximation of the stochastic difference equation. These conditions also serve as sufficient conditions for the stability in probability of the equilibrium points of the initial nonlinear equation. Finally, to demonstrate the validity of the obtained results, some numerical examples and simulations of equations solutions are made and numerous graphical illustrations of stability trajectories of solutions are plotted.

A Cartesian diver to study oscillations and internal gravity waves in a stratified fluid

We propose a variation of the well-known Cartesian diver experiment where, instead of moving in a uniform fluid, the diver floats in a fluid stratified in density. In contrast to the original experiment, for a given external pressure the diver can stop in a stable equilibrium position within the fluid, at the depth where the surrounding density matches its own. By varying the applied pressure, the density of the diver changes and it moves until it reaches a new stable equilibrium condition at a different depth. When a sudden pressure pulse is applied, the diver, pushed off its equilibrium position, starts oscillating due to a restoring force that depends on the density gradient. The oscillations produce internal gravity waves that are typical of stratified fluids, when a portion of them is displaced and transmits its motion to the surrounding fluid. Although they are extremely difficult to observe, gravity waves are particularly interesting, as they typically occur in the atmosphere and in the stars. We propose a simple experiment and suggest a way to make the internal gravity waves visible. The experiment can be realized by students with easy-to-find household objects and used to improve their understanding of many concepts and laws of hydrodynamics, but also to introduce them to complex phenomena of general interest.

Even-odd-layer-dependent symmetry breaking in synthetic antiferromagnets

In this work we examine synthetic antiferromagnetic structures consisting of two, three, and four antiferromagnetic coupled layers, i.e. bilayers, trilayers, and tetralayers. We vary the thickness of the ferromagnetic layers across all structures and, using a macrospin formalism, find that the nearest neighbor exchange interaction between layers is consistent across all structures for a given thickness of the ferromagnetic layer. Our model and experimental results demonstrate significant differences in how the static equilibrium states of even and odd-layered structures evolve as a function of the external field. Even layered structures continuously evolve from a collinear antiferromagnetic state to a spin canted non-collinear magnetic configuration that is mirror-symmetric about the external field. In contrast, odd-layered structures begin with a ferrimagnetic ground state; at a critical field, the ferrimagnetic ground state evolves into a non-collinear state with broken symmetry. Specifically, the magnetic moments found in the odd-layered samples possess stable static equilibrium states that are no longer mirror-symmetric about the external field after a critical field is reached.

Multi-synchronization of coupled multi-stable memristive Cohen–Grossberg neural networks with mixed time-delays

This paper investigates the multi-synchronization issue for a class of coupled multi-stable memristive Cohen–Grossberg neural networks with both additive time delays and distributed delays. First, the multi-stability of the isolated subnetwork with a general class of activation function is analyzed. By employing state-space decomposition, M-matrix and fixed point theory, some sufficient conditions are deduced to ensure that each subnetwork of the coupled networks has (r+1)n locally exponential stable equilibrium states. In the scenario where the time delays are continuously differentiable, a unique Lyapunov–Krasovskii function is established and some sufficient conditions are derived for the coupled system to achieve multi-synchronization under feedback control. Additionally, in circumstances where the time delays are immeasurable or discontinuous, a new feedback controller is constructed based on the system’s model parameters, and a delay-independent finite-time multi-synchronization criterion is proposed. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed methods.

Thermodynamic Stability Theories of Irreversible Processes and the Fourth Law of Thermodynamics.

Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs-Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosion is identified as a thermodynamically stable motion. In the second approach, we use a thermodynamic Lyapunov function and its time rate from the Lyapunov thermodynamic stability theory (LTS, previously known as CTTSIP). In doing so, we demonstrate that the second differential of entropy, a frequently used Lyapunov function, is useful only for investigating the stability of equilibrium states. Nonequilibrium steady states do not qualify. Without using explicit perturbation coordinates, we further identify asymptotic thermodynamic stability and thermodynamic stability under constantly acting disturbances of unperturbed trajectories as well as of nonequilibrium steady states. The third approach is also based on the Lyapunov function from LTS, but here we additionally use the rates of perturbation coordinates, based on the Gibbs relations and without using their explicit expressions, to identify not only asymptotic thermodynamic stability but also thermodynamic stability under constantly acting disturbances. Only those trajectories leading to an infinite rate of entropy production (unstable states) are excluded from this conclusion. Finally, we use these findings to formulate the Fourth Law of thermodynamics based on the thermodynamic stability. It is a comprehensive statement covering all nonequilibrium trajectories, close to as well as far from equilibrium. Unlike previous suggested "fourth laws", this one meets the same level of generality that is associated with the original zeroth to third laws. The above is illustrated using the Schlögl reaction with its multiple steady states in certain regions of operation.

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

We explore the most probable phase portrait (MPPP) of a stochastic single-species model incorporating the Allee effect by utilizing the nonlocal Fokker–Planck equation (FPE). This stochastic model incorporates both non-Gaussian and Gaussian noise sources. It has three fixed points in the deterministic case. One is the unstable state, which lies between the two stable equilibria. Our primary focus is on elucidating the transition pathways from extinction to the upper stable state in this single-species model, particularly under the influence of jump-diffusion noise. This helps us to study the biological behavior of species. The identification of the most probable path relies on solving the nonlocal FPE tailored to the population dynamics of the single-species model. This enables us to pinpoint the corresponding maximum possible stable equilibrium state. Additionally, we derive the Onsager–Machlup function for the stochastic model and employ it to determine the corresponding most probable paths. Numerical simulations manifest three key insights: (i) when non-Gaussian noise is present in the system, the peak of the stationary density function aligns with the most probable stable equilibrium state; (ii) if the initial value rises from extinction to the upper stable state, then the most probable trajectory converges towards the maximally probable equilibrium state, situated approximately between 9 and 10; and (iii) the most probable paths exhibit a rapid ascent towards the stable state, then maintain a sustained near-constant level, gradually approaching the upper stable equilibrium as time goes on. These numerical findings pave the way for further experimental investigations aiming to deepen our comprehension of dynamical systems within the context of biological modeling.

Forming professional reliability of railway power supply specialists

The high level of technological, technical, logistics, organizational and economic changes occurring in the railway industry determines the trajectory of development of professional training of specialists. The priority of safety issues in the context of the complex influence of occupational risks actualizes the scientific understanding of the problem associated with the substantiation of effective characteristics that allow one to withstand the cumulative influence of occupational risks, effectively develop in the professional community, maintaining a stable equilibrium state of the “man – technology – production environment” system. Analysis of research and methodological literature, experience of professional applied physical training at railway universities of the Russian Federation made it possible to identify areas of research aimed at bringing the indicators of psychophysical fitness of specialists into line with the conditions for the implementation of their professional activities. In the structure of professional competence of railway transport specialists, researchers highlight readiness for professional activity. At the same time, in today’s rapidly changing conditions of the professional world, it is necessary to form not only the current (basic) professionally significant qualities of a future specialist, but also to create conditions for the development of potential professional abilities, which will allow effectively confronting risk situations and ensuring the formation of self-regulation mechanisms. The quality that ensures the mobilization and activation of available funds, reserves, sources to achieve set goals, solve problems, and unlock opportunities in a certain area is reliability. In the article it is shown that convergence of play with learning determines the developmental effect of the game method. The complex nature of the gaming method allows to form indicators in the structure of professional reliability of railway power supply specialists.

On thermodynamic stability of black holes. Part I: classical stability

We revisit the classical thermodynamic stability of the standard black hole solutions by implementing the intrinsic necessary and sufficient conditions for stable global and local thermodynamic equilibrium. The criteria for such equilibria are quite generic and well-established in classical thermodynamics, but they have not been fully utilized in black hole physics. We show how weaker or incomplete conditions could lead to misleading or incorrect results for the thermodynamic stability of the system. We also stress the importance of finding all possible local heat capacities in order to fully describe the classical equilibrium picture of black holes. Finally, we thoroughly investigate the critical and phase transition curves and the limits of the classical analysis. This paper is the first in the line of intended works on thermodynamic stability of black holes in modified theories of gravity and holography.