Stable Equilibrium State Research Articles

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.

Airfoil Equilibrium Stability Conditions in the Flow

Airfoil Equilibrium Stability Conditions in the Flow

Critical regularity issues for the compressible Navier–Stokes system in bounded domains

We are concerned with the barotropic compressible Navier–Stokes system in a bounded domain of mathbb {R}^d (with dge 2). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global well-posedness for small perturbations of a stable constant equilibrium state. Our results rely on new maximal regularity estimates—of independent interest—for the semigroup of the Lamé operator, and of the linearized compressible Navier–Stokes equations.

The Future of Sino-Russian Relations in the Russian Far East: A Stable but Not Impervious Equilibrium

Abstract This paper contributes to the ongoing debate on the nature of Sino-Russian relations by applying a multi-vector framework to examine the tenability of the so-called strategic partnership between Russia and China in the Russian Far East (RFE). Addressing a growing body of literature that seeks to move beyond single-factor evaluations of the dyadic relationship, I embrace the principles of analytic eclecticism, borrowing from Voskressenki's (Alexei D. Voskressenski, Russia and China: A Theory of Inter-State Relations [London, 2003]) multifactor framework to advance an argument for intertwining the three dominant international relations research traditions—realism, liberalism, and constructivism—to conduct a more comprehensive evaluation of the current equilibrium in the RFE, rather than assuming in advance the most pertinent lens. This in turn allows for more effective application of international relations theory to Sino-Russian studies. To accomplish my aim, I incorporate data pertaining to economic, geopolitical, and ideational factors. From these data, I find that the relationship in the RFE is in a state of stable equilibrium, with the most important vectors contributing to the balance for each side at present, geopolitical considerations for Moscow and ideational concerns for Beijing, being conducive to cooperation. The short-term potential for conflict is thus minimal, but a shock in the form of increasing Chinese nationalist hostility toward Russia or continued territorial belligerence by Russia internationally would severely endanger the status quo. By applying a similar approach to other dimensions of the Sino-Russian relationship, scholars can gain greater traction in assessing the robustness of the continually evolving bilateral partnership between these two large and important neighbors.

Equilibrium Analysis of Food Safety Liability Insurance and Government Supervision in China

Food safety liability has required consideration around the world. It is realistic to establish a system of food safety liability insurance. However, the existing difficulties include members’ behavior decisions, influential factors, and the responsibility as well as obligations between the players. We build an evolutionary game model to discuss the behavior of food firms and the government in the context of food safety liability and identify evolutionary stability strategy of the participants in the game. Then, we simulate the stable evolution trend of the interaction between food firms and the government using MATLAB software. The results indicate that the initial probabilities of two-party game strategies affect the time length and convergence speed of system evolution but not the overall trend and final result of the evolution. Furthermore, decisions on purchasing food safety liability insurance be affected by the returns of food firms and government supervision. The more severe the punishment for food safety issues, the stronger the sense of crisis among food firms, and the higher probability they will purchase food safety liability insurance. The governance cost of food safety risks plays a role in affecting the strategic decision of the government. The ideal stable equilibrium state of the government and food firms cannot be achieved through spontaneous circulation. Suggestions are given from the perspective of government supervision and punishment to motivate food firms to insure actively.

Magnetically Assisted Rotationally Multistable Metamaterials for Tunable Energy Trapping–Dissipation

AbstractA motif for rotational multistability is developed by arranging permanent magnets in a circular pattern and creating magnet pairs with magnetically induced negative incremental torsional stiffness. Through a set of experimental and numerical studies, different means to tailor the torsional response of a rotational magnet pair are demonstrated. A magnet pair in tandem with tilted elastic arms is harnessed to form an energy‐trapping rotational unit cell. By stacking several of these unit cells upon each other, a 1D rotationally multistable metamaterial capable of storing the input energy and releasing it in the form of rotational waves is developed. The periodic stable equilibrium states in rotational magnet pairs invoke the notion of cyclic multistability, which is employed here to realize, for the first time, a tunable fluid‐free rotary metadamper with energy dissipation induced by repeating snap‐back instabilities. High tunability of magnetic interactions offers a new design paradigm for developing reusable energy dissipative and energy trapping rotary metamaterials, the properties of which can be easily tailored in situ and even at the post‐fabrication stage.

A SIR EPIDEMIOLOGICAL MODEL WITH STABILITY ANALYSIS

A SIR epidemiological model is introduced and analyzed both analytically and numerically. The model possesses a number of stable and unstable equilibrium states which reflects the true nature of a realistic model. Stability of the equilibrium states is discussed by a suitable Lyapunov function. The numerical results are given through graphical representation.

Evolutionary Game Analysis for Grassland Degradation Management, Considering the Livelihood Differentiation of Herders

Grassland degradation has become one of the most important ecological and environmental problems in the world, affecting the ecological balance of grassland and the welfare of residents. To reveal the impact mechanism of herders’ livelihood constraints on grassland degradation, and to explore the comprehensive management methods to ensure herders’ livelihoods and grassland ecological restoration, this paper constructed an evolutionary game model considering local governments and herders. It is found that the ideal stable equilibrium game can be achieved when certain conditions are met, that is, when the local governments actively regulate and herders moderate grazing, the grassland degradation caused by overgrazing can be reduced. The livelihood differentiation of herders significantly affects the stable equilibrium state of the evolutionary game. The local government’s regulation is the key to promoting moderate grazing of herders. The effect of incentive measures on the moderate grazing of herders is limited, while punishment measures can significantly restrict the excessive grazing behavior of herders. Policy support for household livelihood differentiation can effectively motivate herders to moderate grazing and achieve their survival and development needs to a greater extent through a non-grazing livelihood. The research results help decision-makers to formulate policies to combat grassland degradation, and promote the improvement of herders’ lives.

On the role of surface charge and surface tension tuned by surfactant in stabilizing bulk nanobubbles

The abnormal stability of bulk nanobubbles has attracted substantial attention from academia and industry since classical Epstein–Plesset theory predicts that gas bubbles cannot keep stable thermodynamic equilibrium spontaneously. The dual nature of ionic surfactants, acting simultaneously as charge carriers and attenuators of surface tension at the gas–liquid interface, enables them to play a unique role in bulk nanobubble stabilization. Herein the stability of bulk nanobubbles in anionic, cationic and nonionic surfactant solutions over a wide range of concentration is studied. Experimental results show that different kinds of surfactant molecules are involved in the nucleation and stabilization of bulk nanobubbles in different ways. We demonstrate that the accumulation of net charges carried by surfactant ions at the interface is predominantly responsible for stabilizing nanobubbles, instead of the reduction of surface tension. With theoretical calculations, we further quantify the coupling action of interfacial tension and surface charge on the stable equilibrium state of bulk nanobubbles. The result illustrates that the interfacial tension and the degree of gas saturation together determine the upper limit of the bubble size that can exist stably. Our study identifies a route to explore the intrinsic mechanism of bulk nanobubble’s stability.

Study of the Microscopic Mechanism of Natural Rubber (Cis-1, 4-Polyisoprene, NR)/Polyethylene (PE) Modified Asphalt from the Perspective of Simulation.

This paper aims to study the interaction mechanism of waste tire/plastic modified asphalt from the microscopic perspective of molecules. Based on BIOVIA Materials Studio, a classic four-component asphalt model consisting of asphaltene (C149H177N3O2S2), resin (C59H85NOS), aromatic (C46H50S), and saturate (C22H46) was constructed. Waste tires are represented by natural rubber (NR), which uses cis-1, 4-polyisoprene as a repeating unit. In contrast, waste plastics are characterized by polyethylene (PE), whose optimum degree of polymerization is determined by the difference in solubility parameters. Then, the above molecular models are changed to a stable equilibrium state through the molecular dynamics process. Finally, the interaction process is analyzed and inferred using the indexes of radial distribution function, diffusion coefficient, and concentration distribution; further, the interaction mechanism is revealed. The results show that the optimal degree of polymerization of PE is 12, so the solubility parameter between PE and NR-modified asphalt is the lowest at 0.14 (J/cm3) 1/2. These models are in agreement with the characteristics of amorphous materials with the structures ordered in the short-range and long-range disordered. For NR-modified asphalt, the saturate moves fastest, and its diffusion coefficient reaches 0.0201, followed by that of the aromatic (0.0039). However, the molecule of NR ranks the slowest in the NR-modified asphalt. After the addition of PE, the diffusion coefficient of resin increased most significantly from 0.0020 to 0.0127. NR, PE, and asphaltene have a particular attraction with the lightweight components, thus changing to a more stable spatial structure. Therefore, using NR and PE-modified asphalt can change the interaction between asphalt molecules to form a more stable system. This method not only reduces the large waste disposal task but also provides a reference for the application of polymer materials in modified asphalt.

Modeling protein structure as a stable static equilibrium.

We present evidence that the protein structure can be modeled as a stable static equilibrium, determined mainly by compressive supports in the nonpolar interior. That is, protein structures derive their structural strength through the same mechanical principles as do conventional structures like bridges and buildings. This is based on the observation that the experimentally elucidated structural determinants, the interior nonpolar side chains, are engaged in strong compressions in static terms. At the same time, major substructures in proteins, helices and h-bonded strands, because of their geometry, inherently leave gaps in the space they occupy. Under the compressive force, nonpolar side chains from one substructure can protrude into the gaps of another neighboring substructure and block its motion. As a result, interlocking of substructures can form, which builds up the nonpolar core assembly. The native structure then is the one with the structurally most stable core assembly. While intuitively appealing, this is a radical departure from the prevailing thinking that protein native structure is determined by global energy minimum, which is founded on thermodynamic hypothesis. Furthermore, to develop an effective model for analyzing protein structure with conventional tools, a proper mechanical representation must be established. By proving that the stability of the equilibrium in compressive interactions is conditioned on a form of mechanical energy minimum, we show that our notion of native structure can be equally consistent with the thermodynamic hypothesis. By mathematically treating the blocking action, an interaction, as a bar, a physical object, we succeed in representing and analyzing the core assembly as truss, a conventional structure. In this paper we define and expound step-by-step increasingly integrated interlocking patterns. We then analyze the core assemblies of a large set of diverse protein database structures. A native structure can be distinguished from decoys by comparing the composition and strength of their core assemblies. We show the results for two sets of native structures vs decoys.

Estimation of impulse action parameters using a network of neuronlike oscillators

Aim of the study is to develop a method for estimating the parameters of an external periodic impulse action using a spiking network of neuronlike oscillators. Methods. The spiking activity of a network consisting of coupled nonidentical neuronlike FitzHugh–Nagumo oscillators was studied, depending on the parameters of the periodic impulse action. To estimate the amplitude of the external impulse signal, we detuned the FitzHugh–Nagumo oscillators, which were in a stable state of equilibrium in the absence of an external action, by the threshold parameter responsible for the excitation of the oscillator. To estimate the frequency of excitatory pulses, we detuned the FitzHugh–Nagumo oscillators by the parameter characterizing the ratio of time scales, the value of which determines the natural frequency of oscillators. We also changed the duration of external pulses. Results. It is shown that the number of spikes generated by a network of nonidentical FitzHugh–Nagumo oscillators has a monotonic dependence on the amplitude of the external pulse signal and a nonmonotonic dependence on the frequency of the pulse signal. The number of spikes generated by the network remains constant over a wide range of external pulse durations. A method for estimating the amplitude and frequency of impulse action is proposed. The method efficiency is demonstrated in numerical simulations and in a radio physical experiment. Conclusion. The proposed method allows one to estimate the amplitude of an external pulse signal, knowing its frequency, and estimate the frequency of this signal, knowing its amplitude. The method can be used in robotics when solving the problems of information processing related to the motion control of mobile robots.

Buckling of a tilted line of confined hard spheres

ABSTRACT A linear chain of hard spheres confined in a transverse harmonic potential is unstable and buckles, if tilted beyond some critical angle. We examine this symmetry breaking using a computational model that was previously applied to buckling under compression. Results are presented in a bifurcation diagram (in terms of energy as a function of tilt), including both stable and unstable equilibrium states. The key results are consistent with experiments using metal spheres resting in a cylinder.

Uniqueness and stability of equilibrium states for random non-uniformly expanding maps

Abstract We consider a robust class of random non-uniformly expanding local homeomorphisms and Hölder continuous potentials with small variation. For each element of this class we develop the thermodynamical formalism and prove the existence and uniqueness of equilibrium states among non-uniformly expanding measures. Moreover, we show that these equilibrium states and the random topological pressure vary continuously in this setting.

Stability of cross impact matrices

The relationship between drivers and outcomes in technological and social systems is usually difficult to interpret. Pairwise direct impacts between variables can be defined by cross-impact matrices. In research, direct impact matrices' row and column sums are primarily utilized to identify critical, influential, dependent, neuter, and inert variables. In this paper, all existing direct and indirect impact paths between variables are considered, with the aims of finding conditions under which the rank order remains stable (i.e., stable equilibrium state exists) and showing the difference between direct impact matrix and stable state matrix. It is shown numerically that the rank order and thus the categorization of variables can change significantly. A stable state does not always exist, but more direct impacts between variables reduce the risk of instability. The proposed method can support management in strategic planning and decision-making: Management should strive for a stable state that serves to determine the rank order on which informed decisions are based. Caution should be exercised when no stable state exists because the variables cannot be categorized, making the system uncontrollable. Management is advised to incorporate additional impact paths between variables into the system—assuming they were incomplete—which ideally establish a stable state.

Recent evolution of glaciers in the Cocuy‐Güican Mountains (Colombian Andes) and the hydrological implications

AbstractThis study extends knowledge of the evolution of glacier shrinkage in the Cocuy‐Güican Mountains since the maximum glacier extent of the Little Ice Age (LIA). Mass balance data for the Ritacuba Glacier since 2009 were acquired and compared with available data for the Conejeras Glacier (Los Nevados National Park). This study also investigated the hydrological significance of Colombian glaciers, which is still largely unknown because the available information is very limited. Glaciers in the Cocuy‐Güican Mountains covered 13.2 km2 in 2019 compared with 127.8 km2 during the maximum LIA, representing a shrinkage of 89.7%. Analysis of glacier cover observations made in 1955, 1994, 2010, and 2019 revealed that the rate of ice loss was greatest from 1994 to 2010 (0.59 km2 yr−1), and was then almost halved from 2010 to 2019 (0.34 km2 yr−1). This slowing of glacier retreat is consistent with the moderate negative mass balance measured for 2009–2019, and an accumulated loss of 1766 mm w.e. (mm water equivalent). The progressive confinement of glaciers to higher elevations, ice accumulation in topographic locations providing shelter from solar radiation, and an absence of recent marked climatic anomalies could explain why the Cocuy‐Güican glaciers have temporally reached a near equilibrium state conditions. This contrasts with the Conejeras Glacier, where 47,000 mm w.e. has been lost in the same period. The available data on runoff and isotope tracers of streamflow and precipitation suggest that precipitation rather than glacier melt water exerts primary control over the hydrological variability at high elevation sites.

Synthesis of salicylic acid phenylethyl ester (SAPE) and its implication in immunomodulatory and anticancer roles

Salicylic acid phenylethyl ester (SAPE) was synthesized by Zn(OTf)2-catalyzed selective esterification of salicylic acid and phenylethyl alcohol and studied for its role as an immunomodulatory and anticancer agent. Low toxicity and favorable physical, Lipinski-type, and solubility properties were elucidated by ADME-tox studies. Molecular docking of SAPE against COX-2 revealed favorable MolDockscore, rerank score, interaction energy, internal pose energy, and hydrogen bonding as compared to ibuprofen and indomethacin. An average RMSD of ~ 0.13 nm for the docked complex with stable dynamic equilibrium condition was noted during the 20 ns MD simulation. A low band gap predicting a strong binding affinity at the enzyme’s active site was further predicted by DFT analysis. The ester caused a reduction in the percentage of erythrocyte hemolysis and was shown to be non-cytotoxic against human lymphocytes, CaCo-2, and HepG-2 cells by the MTT assay. Moreover, it’s in vitro efficacy in inhibiting COX-2 enzyme under both LPS stimulated intestinal cells and direct sequestration assays was found to be higher than salicylic acid and indomethacin. The anticancer activity of SAPE was tested on the breast cancer cell line MCF-7, and potential efficacy was exhibited in terms of decreased cell viability. Flow cytometry analysis exhibited the arrest of the cell cycle at G1/G0 and S phases, during which induction of autophagic vesicle formation and decrease in mitochondrial membrane potential was observed owing to increased ROS production. Furthermore, at these phases, the onset of apoptosis along with DNA damage was also observed. Pre-treatment with SAPE in colitis-induced Wistar rats displayed low disease activity index and reduction in the extent of intestinal tissue disruption and lipid peroxidation. A marked increase of anti-oxidative enzymes viz., catalase, GGT, and GST, and a decrease of pro-inflammatory cytokines IL-6 and TNF-α in the intestinal tissue extracts of the treated groups was noted. The results of this study have sufficient credence to support that the synthesised ester (SAPE) be considered as an anti-oxidative and anti-inflammatory compound with therapeutic potential for the effective management of cancer.

Memorial stele on a compact spherical support: design-and-engineering solutions, design-basis justification

The article presents the design of the architectural and artistic composition “Memorial stele on a local spherical support” (KB-1 Stele), as well as the analysis of design solutions and the calculated justification of the strength and stability of the KB-1 Stele to external influences in conditions of the most intense climatic influences with parameters set according to building codes and regulations. The design of the KB-1 Stele is a vertically installed overall mass model of a peaceful nuclear explosive device weighing 2.8 tons and 2.8 meters high with hemispherical covers. In accordance with the terms of reference, it was required to preserve the appearance of the device as accurately as possible by placing it on a small local support. The peculiarity of the design lies in its angular mobility relative to the support. To ensure a stable equilibrium state of the stele, a hinge is organized at the place of support, the stele is installed freely by the lower sphere on an intermediate stand with a specially selected spherical surface. Additionally, the center of mass of the stele is significantly reduced by lightening (thinning the walls) of the upper part of the body and installing additional cargo in its lower part. As a result, under the action of external lateral loads, the stele acquires a stable position with possible fluctuations in the tumbler type and with a return to its original state. Analytical and numerical computational studies were performed to substantiate the strength and stability of the KB-1 Stele under external loads. It is shown that the developed design meets the regulatory requirements and is safe in operation.

2PnS-EG: A general two-population n-strategy evolutionary game for strategic long-term bidding in a deregulated market under different market clearing mechanisms

Based on assumptions of bounded rationality and limited information, the evolutionary game theory (EGT) can well describe evolution rule of population behaviors and predict individuals’ decision behaviors. Therefore, this paper focuses on a general two-population n-strategy evolutionary game (2PnS-EG), especially for the general two-population three-strategy evolutionary game (2P3S-EG), and applies it to investigate the evolutionary equilibrium properties of long-term strategic bidding issues in deregulated homogeneous and heterogeneous power generation-side markets (PGMs) under different market clearing mechanisms. First, relative net payoff (RNP) parameters are defined for two types of PGMs. Then, based on RNP parameters, the long-term equilibrium characteristics of 2P3S-EG-based homogeneous PGM bidding are investigated in 4 cases based on theoretical analysis and dynamic simulation. Moreover, long-term evolutionarily stable equilibrium characteristics of 2P3S-EG based heterogeneous PGM bidding are investigated via qualitative analysis and dynamic simulation in the conditions of with and without government supervision, which are then further studied via quantitative analysis and dynamic simulation in two clearing mechanisms of MCP and PAB. Results reveal that MCP is more effective than PAB in guiding PGMs to evolve toward an expected and reasonable long-term evolutionarily stable bidding equilibrium state via adjusting the markets’ RNP parameters appropriately. Finally, the future development of EGT-based strategic bidding issues in PGM is discussed. Overall, the models, methods and conclusions of this paper are practicable and scalable to some extent, aiming to enrich research work on long-term bid equilibrium of PGM, and provide some ideas and theoretical reference for relevant departments and PGMs in competitive on-grid bidding with bounded rationality and limited information.

Nonequilibrium thermodynamic process with hysteresis and metastable states—A contact Hamiltonian with unstable and stable segments of a Legendre submanifold

In this paper, a dynamical process in a statistical thermodynamic system of spins exhibiting a phase transition is described on a contact manifold, where such a dynamical process is a process that a metastable equilibrium state evolves into the most stable symmetry broken equilibrium state. Metastable and the most stable equilibrium states in the symmetry broken phase or ordered phase are assumed to be described as pruned projections of Legendre submanifolds of contact manifolds, where these pruned projections of the submanifolds express hysteresis and pseudo-free energy curves. Singularities associated with phase transitions are naturally arose in this framework as has been suggested by Legendre singularity theory. Then, a particular contact Hamiltonian vector field is proposed so that a pruned segment of the projected Legendre submanifold is a stable fixed point set in a region of a contact manifold and that another pruned segment is a unstable fixed point set. This contact Hamiltonian vector field is identified with a dynamical process departing from a metastable equilibrium state to the most stable equilibrium one. To show the statements above explicitly, an Ising type spin model with long-range interactions, called the Husimi–Temperley model, is focused, where this model exhibits a phase transition.